Normal tyre and inner tube systems need no adhesive.
You glue tubular tyres (really old fashioned or super high performance), some modern tube-less tyres (like Stans) and you glue some rim tape to the rims (Velox).
You need studs on icy surfaces, knobbles on snowy surfaces and normal commuter tread on wet roads but many riders use normal tyres in the snow. Repairs in the cold are unpleasant so use the toughest tyres you can find.

You normally wear a bit less insulation on a bike than for walking and you tend to distribute it differently but basically you can wear the same. Jeans are bad, soaking up water, slow to dry, with thick seams.

Beater bikes often survive better left out in the cold all the time. Water can condense inside the frame and cause internal rust. Winter bikes are often dirty and unwelcome indoors. I put a plastic bag over the saddle and seat-post to keep rain out. Security is a different issue.

The best Beater bikes started life as decent quality, midrange models and are still quite good. A bad new bike will always be bad and will only get worse with age.