Will Synthetic Field Boots get ruined by the snow?

They shouldn't. I have the same brand and I've gotten them wet many times. They are very waterproof and hold up well. I make sure to dry them off though because I show in them and I don't want any mold or weak spots. I'm pretty sure that they are made to be very waterproof. They are made to be washable, so I would imagine they can handle a little snow. I've always wondered what they mean by washable, but I've never stuck mine in the washing machine to find out.