Dec and Jan are coldest months , there are many locations here which would give perfect snow covered views. Do carry warm clothes on your visit. Also confirm the route is not closed at very high altitude spots because of snowfall before travelling.
Some place recommendations:
Chitkul
Reckongpeo
Barot valley
Prahshar lake
Hatu Peak
Manali
Shimla
Thank you
There are so many good hostels in Goa, you can choose according to your location preferences. Zostel/ Happy panda (arambol), the crazy hostel (anjuna), summer by thehostelcrowd (palolem), backpackers panda (candolim) and many more.
Zostel, Moustache, Backpacker panda, are well known and nice hostels, other than this if you check out places and streets around Zostel you'll come across a lot of cafe/stays
Around 800-1k... but it'd be better if enquire at places on the outskirts of chandigarh ...as in not the main city.. they would give u a good deal
... goodluck