Lassen NP has always been one of my favorite NPs - summer and winter - a huge variety of terrain and the most varied and weird geology outside of Yellowstone. But more so because it is so little visited. Even while car camping and seeing the road-side attractions, if you spend a few days you start to recognize a bunch of people, it's that little visited. Totally unlike Yosemites or Yellowstone or GCNP in that way.
With so little snow, you could do some cold, non-skiing BP trips. Talk with the rangers carefully about routes and check weather forecasts closely. 1-2-3 day trips ought to be fine. I'd be nervous a week out without weather updates because if snow ever does come, it could change a trip instantly.
Get online or the phone and check Lava Beds NM - an even small unit. Crawl around underground - they have 300 caves with a dozen of the larger ones developed for easier access (parking above, stairs to the flattish floors below. In the 105F summer a 40F cave is a wonderous thing. Likewise on a -10F day!
I'd skip Shasta unless you're ready for some big mountain contingencies. I've been up it, done many other 14ers, and done a lot of snow travel / camping (live in Alaska) and I'd be really leary of going to 14,000 in Feburuary. Being only 10,000 feet and with an approach ski/hike on a road, Lassen as a peak is much more accessible - I've skied up it in March from the ski area and back in a not long day. But even without the peak bagging, there's so much more to see around Lassen and Lava Beds than around Shasta, IMO.