No, by all means, go. Even if your hunt turns into a scouting trip for next year.
Remaining wild birds will generally be pretty skittish but the snow can be to your advantage (other than they aren't walking around much and leaving scent.) Head towards the thick stuff, cat tails, etc. at this time of year.
You can go all day without seeing any and then suddenly get your limit in 15 minutes in weather like this...or you could just go all day without seeing any...Either way, enjoy the time with your dog. It really isn't all that cold, anyway.