Is the term "ice cream" considered one word or two?

My question is a little broader than the title and applies to a term which is described by more than one "word". Is the term (in this case "ice cream") one word, or two?

Based on my research, the three dictionaries that I consulted, Merriam-Webster (MW), MacMillian (MM), and the Oxford Dictionary (OX) all seem to provide some leeway in expressing exactly what a word is and if it must be delimited by spaces and/or punctuation. See definitions below:

MW(b)(2): "any segment of written or printed discourse ordinarily appearing between spaces or between a space and a punctuation mark"

OX 1a: "single distinct meaningful element of speech or writing, used with others (or sometimes alone) to form a sentence and typically shown with a space on either side when written or printed"

MM 1: "[countable] a single unit of written or spoken language"

MW and OX use words like typically and ordinarily indicating that there is the possibility for multi-word words, but don't exactly provide sample sentences with any. Even MM doesn't quite spell out what comprises a single unit. However, I would argue that "ice cream" independently, that is, taken as two separate words, is two units of language, rather than one.

Even in looking up compound word examples, these are delimited by a space on either side, that is, condensed into one clear-cut word by means of placement (such as backstab) or they use a hyphen (such as white-collar).

With this predicament in mind and as a yes or no question (providing justification), is "ice cream" as is, no hyphen and not stuck together as "icecream" or "ice-cream", one word, or two?

Solution 1:

We never say, I want an iced cream, or cream with ice, or cream which is iced, or anything else. We just say, I want ice cream. My point is when something is un-modifiable, that means it exists as a single unit. It may appear to have two words, but those two words, spoken separately, would have different meanings, so that particular word needs to be spoken in one breath to convey a particular meaning. So 'ice cream' is a one word. It has a distinct meaning.

Now consider, 'beautiful day.' Both Beautiful and Day have their own separate meanings and spoken together they convey a different meaning. Yet 'beautiful day' is not one word, because same can be expressed differently like, lovely day, pleasant day, awesome day, etc. More importantly, in 'beautiful day,' beautiful is an adjective. And if we start representing ice cream as having two words, would we say ice is an adjective here?

Solution 2:

When you're speaking, you stress an adjective-noun combination differently from a compound noun. This is what makes the following children's joke work:

The red house is on the corner. The blue house is next to it. Where is the white house?
I don't know. Where is the white house?
The White House is in Washington, D.C., of course.

For another example, in the math video "Not Knot", the narrator pronounces "a whole number" like it was an adjective-noun combination, and not a compound noun. That something was wrong was glaringly obvious to me the first time I watched it (although it took me a while to figure out exactly what).

"Ice cream" is pronounced as a compound noun.