Depends how much snow there is, really. You can go over pretty much anything, but going through will be another story. Tall weeds pushing up above the snow will cause more resistance on the snowshoes as you try to pull through, making walking more difficult. Of course all this is relative, because it may still be easier than walking through 2 feet of snow and weeds in regular boots!
I was out yesterday 'shoeing around the nature preserve behind my house and I had no issues whatsoever. I just floated right over the top of everything. Cattails would be out of the question, though.
A lot may depend on your indidual coordination as well.
Check with local sporting goods stores, as some may rent snowshoes out for a nominal fee. This would give you the chance to try before you buy.