If they are coming out--you will easily see it,especially with fresh snow.The water from their bodies will freeze and an ice slick will form.
While they will travel under the ice,unless their are dens or lodges fairly close,you may not have them using the open spotd.
I have taken beaver that came a long ways under ice--close to a half mile, but it can be a hit or miss thing.And it sounds like your open areas are misses.
Tom