This is actually good moment, maybe a tad too late to get winter tires. Because of the steep slopes in Praha you should need studded tires in midwinter. As to clothes, you need actually less coverage in riding than in walking, as you generate heat at a faster rate. However, loose regular clothes and shoes are preferred to any tightly adhering fashionable cycling attire. In winter you need lower gears, but presumably you already have them riding in the hilly area.