"Clouded" vs "clouded over."

Solution 1:

My mind clouded with murky thoughts.
My mind clouded over with murky thoughts.

At face value, they are equivalent. From the OED:

Cloud

(of the sky) become overcast or gloomy.
‘the blue skies clouded over abruptly’

Note how the definition does not mention "over", yet the example does use it. This seems to imply that using "over" is optional, and not required to achieve grammatical correctness.

I would be more inclined to say "clouded over", but I think that's subjective and not relevant as to whether one is more correct than the other.

Edit I am aware that the definition I linked specifically mentions that it pertains to the sky. However, I feel that figurative usage applies here. Especially since the definition includes "gloomy", which is already often used to describe the feeling of sadness, not only the state of the weather.

Solution 2:

You're running into trouble with metaphors here. When we use language like this we (consciously or not) create a metaphor. Think about what the metaphor means: what is "your mind" in this metaphor?

Let's look at the second example: "My mind clouded over with murky thoughts." Is your mind a sky in this metaphor? A sky "clouds over", meaning clouds come in and block the view of the sun (or stars), for an observer standing on the ground. This metaphor is already confusing. Who is the observer? If your mind is the clouds, who is looking at them? Do they have their own mind, with their own thoughts?

Let's look at the first "My mind clouded with murky thoughts.". The verb "to cloud" is legal so "clouded" can mean the past form of the verb. So, in this metaphor, your mind is more like a container of some kind which has become cloudy. One might think of a fish tank, or a bottle, or some other kind of glass-walled container. This metaphor is better, in that you're saying "My mind is like a cloudy fish tank and it's hard to think properly because I can't see the "contents" very well."

However, there's a language problem with this sentence: this usage of "clouded" isn't very common (except as part of 'clouded over' perhaps). What is much more common is "clouded" as an adjective, to mean "having lots of clouds". If the reader makes this assumption then the sentence is ungrammatical: it looks like it needs a "was", as Steve Benner suggests above, ie "My mind was clouded with murky thoughts."

So, the difference is in the metaphors, I think, but both have their own issues.