Is there a term for simultaneous snow and rain?
Solution 1:
Sorry, I believe the answer is "sleet":
Rain and snow mixed (also known as sleet) is precipitation composed of rain and partially melted snow. This precipitation can occur where the temperature in the lower part of the atmosphere is slightly above the freezing point (0 °C or 32 °F). Its METAR code is RASN.
Meteorologists around my geographical area (New England) refer to it as a "wintry mix" most of the time. But it's clear that "sleet" is what is meant here.
From the Wikipedia entry for rain and snow mixed.
Solution 2:
It's not sleet — that's tiny ice pellets which generally fall in winter. Hail is also ice pellets, but they are produced by a different meteorological process, and can occur any time of year.
If there's a word for snow and rain at the same time, it's so obscure that the weathermen around here (Boston) don't know it. This often happens when it starts raining, and then becomes cold enough to snow, or vice versa. The weather reports usually call this "rain changing to snow", "snow changing to rain", "a mix of snow and rain", or "a wintry mix".
UPDATE: While it seems that nowadays, some people use sleet for a mixture of snow and rain, this is the original meaning of sleet. From the Encyclopaedia Perthensis, Edinburgh, 1816:
SLEET. n. s. [perhaps from the Danish, slet.] A kind of smooth small hail or snow, not falling in flakes, but single particles.
Solution 3:
With regard to the dispute over what exactly sleet is, I note that Dialect Notes, volume 4, part 4 (1916), devotes an entire page to a communication received from the chief of the U.S. Department of Agriculture’s Weather Bureau, which states:
Sir: There has been some discussion in this Bureau as to the way the term “sleet” should be used for official purposes. A search of dictionaries and of a large amount of technical and non-technical literature appears to establish the following facts:
(1) In England “sleet” means usually, though not invariably, a mixture of raindrops and snowflakes.
(2) In this country the term “sleet” has nearly always been applied in the meteorological literature to some form of water which is in a frozen state before reaching the ground; viz., either small particles of clear ice (often mingled with rain or snow), or little snow-like pellets, differing in structure from true hailstones, but often called “winter hail,” or “soft hail.” (In German the latter form of precipitation is commonly called Graupel, and this name is sometimes used in English texts. The French equivalent is grésil.)
(3) Non-meteorological usage in this country varies; comprising the uses noted above under (1) and (2), and also another, in accordance with which the term “sleet” is applied to a coating of ice on terrestrial objects formed by rain which freezes after contact with such objects. When this coating is heavy, and especially when it results in the breaking of branches, wires, etc., the phenomenon as a whole is often called an “ice storm.” This use of the term “sleet” is common in the newspapers, and also in engineering literature, particularly in reference to accumulations of ice, due to rain, on wires and rails. In England the specific name for this form of ice is usually “glazed frost,” and this term is used officially by the British Meteorological Office. The name “silver thaw” has also been applied to it, in both Great Britain and the United States, but this expression is so inappropriate and misleading that it is avoided by most scientific writers.
The Bureau will feel indebted to you for any information you may be able to supply as to the use or uses of the term “sleet” current in your vicinity, and also as to the meaning which, in your experience, most commonly attaches to the term in contemporary speech and literature. Information would also be appreciated concerning the etymology and history of the word “sleet,” in case you are able to add anything to what is found in the latest editions of the New English, Century, New International, and Standard Dictionaries.
Very respectfully,
C. F. Marvin, Chief of Bureau
United States Department of Agriculture, Weather Bureau
So in all likelihood conflicting definitions of sleet go back at least a hundred years.
Solution 4:
To make it easy to compare the terms for all forms of ice-containing precipitation used by US weather scientists, I have pulled together the following comprehensive list of such terms from the meteorological glossary of weather.com. (Strangely, the 'wintry mix' that others have also mentioned in their responses doesn't appear in this glossary, even though I have often heard it from the lips of US weather forecasters — including those of the Weather Channel.)
Note that this list accordingly has a bias towards US usages. As others have remarked in their answers here, some of the terms, such as sleet, are applied differently in Britain; unfortunately, there doesn't currently seem to be a corresponding list on the website of the UK's Meteorological Office. (If there is, I could not find it.)
FREEZING PRECIPITATION
Precipitation that is liquid, but freezes upon impact with a solid surface, such as the ground or other exposed surfaces.FREEZING RAIN
Rain that falls as liquid and freezes upon impact to form a coating of glaze on the colder ground or other exposed surfaces.FROST
The covering of ice crystals that forms by direct sublimation on exposed surfaces whose temperature is below freezing.GRAUPEL
A form of frozen precipitation consisting of snowflakes or ice crystals and supercooled water droplets frozen together.HAIL
Precipitation that originates in convective clouds, such as cumulonimbus, in the form of balls or irregular pieces of ice, which comes in different shapes and sizes. Hail is considered to have a diameter of 5 millimeter or more; smaller bits of ice are classified as ice pellets, snow pellets, or graupel. Individual lumps are called hailstonesHOARFROST
Another name for frost. A deposit of hoarfrost occurs when air with a dew point below freezing is brought to saturation by cooling.ICE CRYSTALS
Precipitation in the form of slowly falling, singular or unbranched ice needles, columns, or plates. They make up cirriform clouds, frost, and ice fog. Also, they produce optical phenomena such as halos, coronas, and sun pillars. May be called "diamond dust."ICE PELLETS
Precipitation in the form of transparent or translucent pellets of ice, which are round or irregular in shape. They have a diameter of 0.2 inches (5 mm) or less. They are classified into two types: hard grains of ice consisting of frozen rain drops or largely melted and refrozen snowflakes; pellets of snow encased in a thin layer of ice which have formed from the freezing of droplets intercepted by pellets or water resulting from the partial melting of pellets.ICE STORM
A severe weather condition characterized by falling freezing precipitation. Such a storm forms a glaze on objects, creating hazardous travel conditions and utility problems.RIME
The rapid freezing of supercooled water droplets as they touch an exposed object, forming a white opaque granular deposit of ice. It is one of the results of an ice storm, and when formed on aircraft it is called rime icing.SLEET
Also known as ice pellets, it is winter precipitation in the form of small bits or pellets of ice that rebound after striking the ground or any other hard surface.SLUSH
Snow or ice on the ground that has been reduced to a softy watery mixture by rain and/or warm temperatures.SNOW
Frozen precipitation in the form of white or translucent ice crystals in complex branched hexagonal form. It most often falls from stratiform clouds, but can fall as snow showers from cumuliform ones. It usually appears clustered into snowflakes.SNOW GRAINS
Frozen precipitation in the form of very small, white, opaque grains of ice. The solid equivalent of drizzle.SNOW PELLETS
Frozen precipitation in the form of white, round or conical opaque grains of ice. Their diameter ranges from 0.08 to 0.2 inch (2 to 5 mm). They are easily crushed and generally break up after rebounding from a hard surface, unlike hail. Sometimes it is called small or soft hail.THUNDER SNOW
A wintertime thunderstorm from which falls snow instead of rain. Violent updrafts and at or below freezing temperatures throughout the atmosphere, from surface to high aloft, discourage the melting of snow and ice into rain. Intense snowfall rates often occur during these situations.
Solution 5:
According to Weather.com's glossary of meteorological terms, sleet is:
Also known as ice pellets, it is winter precipitation in the form of small bits or pellets of ice that rebound after striking the ground or any other hard surface.
It's not a single word, but the term I have seen used for mushy snowflakes on Accuweather.com and other weather forecast sites is often rain with snow flurries, defined as:
Light showers of snow, generally very brief without any measurable accumulation
A heavier version of snow flurries is snow showers (which is considered to be different from snow fall):
Frozen precipitation in the form of snow, characterized by its sudden beginning and ending