I have analyzed historical records for Mammoth in some detail for this question, which illustrates the impact of Sierra snowfall volatility:
December 15 is probably the median date for which Mammoth becomes worth the trip for me, based upon the historical data of opening terrain. But terrain usually doesn't open gradually because Sierra storms tend to be erratic but large. Mammoth will often go from <20% open to >70% after one substantial storm.
42-Year Data
For Dec. 1
36% of the time 20% or less of the mountain is open
31% of the time 25-40% of the mountain is open
19% of the time 50-80% of the mountain is open
14% of the time 90+% of the mountain is open
For Dec. 15:
17% of the time 20% or less of the mountain is open
21% of the time 25-40% of the mountain is open
24% of the time 50-80% of the mountain is open
38% of the time 90+% of the mountain is open
For Jan. 1:
10% of the time 20% or less of the mountain is open
7% of the time 25-40% of the mountain is open
16% of the time 50-80% of the mountain is open
67% of the time 90+% of the mountain is open
For Jan. 15:
5% of the time 20% or less of the mountain is open
7% of the time 25-40% of the mountain is open
9% of the time 50-80% of the mountain is open
79% of the time 90+% of the mountain is open
For Feb. 1:
5% of the time 20% or less of the mountain is open
5% of the time 25-40% of the mountain is open
5% of the time 50-80% of the mountain is open
85% of the time 90+% of the mountain is open
How does Tahoe compare? Most of the places on the Sierra Crest get more snow, but all of them except Kirkwood are much lower and thus get occasional rain and do not preserve as well. Overall I'd say Kirkwood might be a touch more reliable early season than Mammoth and Sugar Bowl and Alpine similar to Mammoth. Elsewhere I think there may be as much of a 1/3 probability of less than half terrain being open, which is not the way I would bet premium-priced holiday $.
The big places, Squaw and Heavenly, are among the least promising. Squaw, because it's so steep and needs 6+ feet of coverage for much of its terrain. Heavenly is leeward of the Sierra Crest and gets less snow. Mott/Killibrew Canyons open on average in late January.
Your instincts are correct that NM is a really bad idea that early in the season. Denver is more consistent but overall I'd be inclined to take my my chances with Tahoe because of the flip side of that volatility. The top 1/3 of Christmases at Tahoe are full operation with far deeper snowpacks than you ever see that early in Colorado. The exception would be Steamboat, which has an excellent early season record, better than Mammoth's. Vail's is quite good too, but I'm guessing you're not willing to pay Vail holiday prices. Summit County has lesser snowfall/likely terrain open and the worst crowds.
With respect to crowds at Tahoe, traffic is the most chronic issue when it's busy. If you can get your group organized in the morning and arrive very early at the ski area of your choice, it's usually manageable. In terms of on-the-mountain Heavenly's awkward layout and location near the cheapest and most abundant lodging make it the least pleasant Tahoe area when it's busy IMHO.
So within your FF choices I would vote Steamboat first (rent a car and drive the ~4 hours from Denver) and Reno/Tahoe second. If you do Tahoe be aware that you'll be daytripping in the car nearly every day and need to be organized for that, possibly including 4WD. An alternative is to rent the car in Reno and drive 3+ hours to Mammoth, where you won't require daily commuting (shuttle buses are available) and somewhat better snow reliability as detailed above. Crowd/congestion issues at Mammoth Christmas week are not bad for the advanced upper areas, but it's very congested for low end skiers around the lodges. Recall a few years back GPaul spent 2 weeks in the Sierra over the holidays enjoying Mammoth much more than Tahoe.
SLC is vastly superior to any of the above for Christmas week.
1) Snow reliability in LCC/BCC is much better.
2) SLC is a city so holiday price gouging for lodging is mitigated (true to some extent for Reno also).
3) More and better secondary ski areas are available to escape crowds in Utah.
4) Daytrip car commuting is much less congested and/or subject to weather issues than at Tahoe.
Crunch the numbers and you may find it's better to go to Salt Lake and use the FF miles some other time.
