1. Emily likes winter because she can see snow in the mountains.

2. Emily likes winter because she can watch snow in the mountains.

3. Emily likes winter because she can look at snow in the mountains.
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Which verb should we use?

All three might be appropriate. If Emily can see mountains in the distance, "see" is good. If she is in the mountains and can "watch" snow fall, that is appropriate. To "look at" and "see" mean the same thing.