I live in Canada and got my dog in February and there was snow until mid may. For me it was great. He wanted to do his business, but he loved the snow. Now I don't have a prissy dog who does not want to step in wet grass, etc, he loves it all, sleet snow, sune, rain etc, he goes out in it all and loves it!
It is also easier house training because you can see in the snow they went, sometimes the males do to much marking! He also did a lot less sniffing around so I did not need to stay out there long. We live in an apartment building, so I had to put on my whole getup every 30 minutes when he was a pup and go outside, trust me if I can do it that way you can!
As for socializing. I tried to keep charlie away from most dogs until he had all his shots. I then started doing to pet stores a lot more for socializing or taking a walk in the snow. We would always run into larger dogs that needed there long walks. Socializing was not that big of an issue for us, but shih tzus are normally very friendly dogs.