I will show you a little trick I use whenever I have a problem with fuzzy primer on my miniatures. It's easy to do and you probably already have what you need to do it. This can save you from stripping the model.
Here's a step-by-step tutorial on how to create miniature ice effects on bases using Vallejo Still Water. It's cheap, very simple to do, and it's a great way to really enhance any snow basing you're doing. Check it out!