I've done only a few routes in the winter in the Sierra, including Winter Route on Lone Pine Peak, the NE Ridge of Bear Creek Spire, and the East Buttress of Whitney, but voila my experience: winter routes in the Sierra consist mostly of rock climbing with approaches conveniently covered in snow. If you ski or are otherwise comfortable on snow, this means fast approaches! It's awesome. The climbing itself will be normal rock climbing with snow in sometimes inconvenient places, and it will be colder than usual. One usually climbs in boots, but when you're not in the shade, it can be reasonable to climb in rock shoes. If it has snowed recently and the rock is still dusted, you will have to climb with crampons on. This makes the climbing feel significantly harder, since Sierra granite tends not to have the best features for dry-tooling, but it's not at all unreasonable. Depending on the amount of snow and ice and the rock features, you will either have to climb with two tools, one tool and one hand, or two hands. It just depends. The following picture is of NE ridge of BCS, and I assume from your post that you want to climb routes in conditions like these:
Or these:
If you've done the 5.7 first pitch on the headwall above Winter Route and Summer Ridge on the south face of LPP, that pitch is pretty easy 5.7 face climbing in the summer, but with crampons on it feels like 5.9 or 10. I needed to use tools often on that pitch, since the slabby, dusted rock had few useful holds for be-gloved hands. I did half of the East Buttress route in boots (Nepals) and half in rock shoes when it warmed up, but it was dry enough that we climbed with hands only. We kept boots and crampons on for the entire NE ridge of BCS, since it had snowed two feet the previous day, and we had two tools for the leader and one for the follower. This picture is on the 5.7 headwall pitch on LPP:
This is the gear I've found useful both in the Sierra in winter and at Tahquitz in the winter: two tools, umbilicals, a set of old crampons (you will do very little ice climbing in the Sierra, so expect your points to get blunted by rock), a few good pairs of gloves (OR Vert, Extravert, and MH Hydra are some of the best), usual rock gear (but throw in some hexes for bashing into icy cracks), a screw or two (depending on route), no pickets, and a few pitons (icy cracks will sometimes take nothing else--knifeblades are the most useful).
I think the general rule of thumb is that alpine conditions in the Sierra aren't as awesome as they are in the Alps or Canadian Rockies or other comparably-sized ranges, since we never get any damn ice, but they are still plenty fun. Have at it!