My winter bike is, like you said, an old MTB that I already had on hand. I followed sixty fiver recipe for DIY studded tire, made myself two beautiful rear panier, one out of a cat litter bucket and the other with all time favorite rubbermaid countainer. Total cost: less than 60$. I went to work with it 20 times approx. last winter. It's heavy and slow but I intend to keep it for a few more winters.

The tires are 26x1.75. when the road are clear I inflate them to the recommended maximum pressure of 65 psi so the studs don't make contact with the pavement so there's a lot less drag. When the roads are icy I deflate them to about 25-30 psi so the stud make full contact, very good grip but very very slow. Last winter I only had to deflate my tires once or twice and didn't fell off at any time.