The difference is largely one of connotation. The verb to shroud derives from the noun shroud, which typically refers to a sheet used to cover the dead for burial in some religious traditions. Because of this association, when you say that something is shrouded with or shrouded in, it connotes an atmosphere of mystery, gloom, or the numinous.
Shrouded in also lends itself more readily to metaphorical usages. You might say that "The castle was shrouded in mist", but it would sound odd to say that "The castle was covered in mist".
If you go by Wikipedia,
In topography, a summit is a point on a surface that is higher in elevation than all points immediately adjacent to it. Mathematically, a summit is a local maximum in elevation. The topographic terms "acme", "apex", "peak", and "zenith" are synonyms.
According to this glossary,
The summit is the highest point.
In theory, every mountain has exactly one summit. In practice, mountaineers will in many cases talk about multiple summits (eg Everest South Summit), thus blurring the distinction between "summit" and "peak".
Sometimes as you're climbing you'll approach a spot that looks like it might be the summit, only to discover it's a "false summit".
The word comes from Latin "summus", meaning "highest".
In the 19th century, "summit" was also applied to other kinds of highest points, such as the highest point reached when crossing a pass.
The same glossary has an entry for peak:
A peak is a point that's higher than all other adjacent points. In mathematical terms, it's a local maximum, the point with slope of zero along a convex-up curve. The thing to understand about this definition is that it is entirely localized: there may be some higher point not far away, but if you can't get there without going downhill first, you're standing on a peak.
In other words, most mountains will have multiple peaks.
So, to sum it all up, unless you are particular about not piquing the interest of some topographical fusspot, it appears that there's nothing wrong in using the two terms interchangeably. However, technically speaking, a mountain can have only one summit, but multiple peaks. It follows that the lone summit is also a peak :)
Best Answer
The meanings are very similar, and these three prepositions can be used almost interchangeably, particularly in the context of your "The mountain is covered with/in/by snow" example. But some subtle nuances may apply.
When referring to a substance that sticks to another, use in or with, but not by:
Another example:
When referring something that physically protects something else, use with or by, but not in:
Use covered with to indicate an unusual amount of something on top of something else; use covered by to connote a covering so dense that the object being covered is completely obscured from view:
Another example:
Somehow, the latter (covered by) paints a picture where the butterflies are so close together that I can hardly any the grass at all, but in the former (covered with), I picture a lot of butterflies, just not necessarily so many that I can't see the grass.
When talking about metaphorical coverage, use covered by:
Another example:
Other guidelines are likely to apply as well. This is not a question with an easy and straightforward answer.