The series of switchbacks at Bunnel Point (sp?)--just after the two bridges that cross the Merced River about five miles up from LY valley campsites--can be dangerous, depending on conditions. For two reasons. First: it's not at all obvious, but there's avalanche danger from above. Study your map here. Second: there's a serious icing problem here. For a very brief section, that's nevertheless dangerous, it can become difficult to get grip without crampons or microspikes. It all depends on how snow and weather unfold. If you're bringing an ice axe, you're fine.
There's also avalanche hazard at the bridges.
There can also be a tricky stretch just before the final bridge re-crossing the Merced a mile and a half or so beyond the switchbacks I just described. It's steep and if icy, and you slip, you go into the Merced just before a series or waterwheels. And there's no way around it. You won't survive. It's a short stretch and soooo enticing because you just know that you're going to make it....
Both of these sections go through freeze/melt cycles that are conducive to ice. The switchbacks are worse: meltwater flows onto them from above during the day, and that freezes at night.
Otherwise this can be a delightful trip, just beautiful, you won't regret it if the weather cooperates! And think about day-tripping up towards Vogelsang pass. Honestly, if you can, plan an extra day for this. It's the best part of the venture; well worth it. You may be surprised at how this south facing, sun exposed section is snow-freeish.
Wait, late Dec.-early Jan. is typically one of the stormiest period in the Sierras.
Seriously check the forecast. Are you familiar with the Sierras in winter? I personally would never set in stone a winter trip in that time frame if I was coming from out of the area.
EDIT: geeze, I forgot: the stretch from Happy Isles to the top of Nevada Falls can be icy, especially along the mist trail! Very steep here, and awful if icy.