Earlier this year I had a lot of fun riding in Oxford when there was all the snow. Was riding a knackered old mountain bike with fairly knobbly tyres.
As above make sure you are visible and have decent lights. Having two of each is always a good idea in case one fails (you can always clip an extra rear one to your backpack or helmet).
If it looks like it could be icy take extra care, especially if you are riding on slicks. Try to stick to gritted roads and avoid manhole covers etc. more than usual. Be extra assertive with your positioning, motorists rarely factor in weather conditions when passing cyclists.
Make sure your brakes work/tyres inflated/all the usual.
Try to relax as much as possible, if you tense up you are more likely to be caught out if you hit an icy patch.
For cycling in snow:
Knobblies are best
For fresh snow - use a high gear to avoid spinning the rear wheel, try to follow other wheeltracks, avoid making abrupt steering motions and let the bike go where it wants to, relax.
Slushy snow is much trickier. It builds up everywhere on the bike, between the tread on the tyre, in the brakes etc. Difficult to get going again if you stop so try to keep momentum. As much fun as cycling through it is, sometimes quicker to walk through it.
Compacted/re-frozen snow isn't too bad actually as long as you stay relaxed and cycle confidently. It provides a decent amount of grip so just stick within your limits.
Ice on the other hand is deadly and difficult to spot. So best tip is probably just to take it easy and if you feel yourself sliding then try to go with it and avoid abrupt steering. Give extra distance to other road users in front.
Also wrap up warm. Gloves and a hat if you aren't wearing a helmet are a must. However dress in thin layers which you can take off rather than thick clothes, as you can get surprisingly warm even when it is freezing outside.