The answer is probably not during the period of reliable snow records at Alta-Guard, which begin after WWII, but there are a few nuances to consider, especially with regards to snowpack.
What we know is that this winter the Dec-Feb period was the warmest on record (since 1895) in the northern mountains climate zone that includes the Wasatch and Uinta Mountains. The closest analog in the instrumented record is 1933/34, but that was before reliable snow records at Alta-Guard. The only other Dec-Feb period with temperatures close to this winter is 1980/81. More on that season in a minute.
What about March? Well, the temperature records for this March are still trickling in from volunteer observers. Through yesterday, though, we were running well above average. In terms of where we were through from December through the end of astronomical winter on Friday, there's a good chance it was the warmest such period on record.
With regards to snow, the Utah Avalanche Center reports that Alta-Guard has has had only 213.5 inches of snow since November. It looks like we're going to get some snow Monday-Wednesday. I'm not sure how much, but for the sake of argument, let's suppose it goes big and we end up with 250 inches through the end of March. The only other winters with less than 300 inches from November –March are 1960/61 (291 inches), 1962/63 (265 inches), and 1976/77 (283.5 inches). Let's also throw 1980/81 into the mix since it is the closest temperature analog. In that low snow year, the November–March snowfall was 339 inches.
But let's look at the March snowfall in those years specifically. In 1960/61, 1962/63, and 1976/77, and 1980/81, the March snowfall was 113, 93, 129, and 110 inches, respectively. These were drought years, but they rallied at the end, producing above average snowfalls in March. That's not going to happen this year, even with the storms Monday–Wednesday.
Thus, the combination of low snowfall and high temperatures for December to mid March appears to be unprecedented since record keeping began after World War II.
However, we haven't looked at snowpack yet. Ideally, one would look at manual snowpack water equivalent observations for which there are records at some sites in the Wasatch that extend back to before World War II. I don't have easy access to those records, and often they are collected around April 1st, so I'm going to leave that as an assignment for you weather sleuths and instead look at shorter-term records from SNOTEL stations. Unfortunately, these don't extend back to 1980/81, but they do go back to 1989 or so for most central Wasatch sites.
At the Mill D North SNOTEL, the snowpack has already ripened and begun to melt (green line) this year, which is quite remarkable (green line). We've already lost about 3 inches of water at this site to melt. Curiously, the winter of 1991/92 has a peak snowpack water equivalent that is only slightly higher than this year, even though we are way behind in snowfall amount at Alta-Guard. During that season, the Alta-Guard Nov-Mar snowfall was 367.5 inches. More on this in a minute.
The Brighton SNOTEL shows similar behavior, with 1991/92 also being the next lowest season.
Now lets shift to Thaynes Canyon (Park City) and Snowbird. Both of these sites are on north-facing aspects and thus the melt has yet to begin in earnest. Again we see 1991/92 raise it's ugly head as the next lowest season. In fact, snowpack water equivalent at Snowbird is right on top of that year as of Friday.
So, we sort of have a mixed bag when it comes to snowpack water equivalent observations, although most are well behind 1991/92. How to explain the snowpack observations, especially at Snowbird?
Welcome to the world of observational uncertainty and the comparison of apples and oranges. SNOTEL observations are affected by changes in site characteristics and instrumentation. They are also a measurement at a single point and in any one season, wind transport and other factors can play a role.
Such issues affect other observations we've used here. For example, the Alta-Guard snowfall observations are affected by changes in measurement location or techniques. In addition, we are comparing seasonal snowfall observations (the sum of new snow depth observations taken daily or even more frequently) as opposed to snow water equivalent observations. The latter are more important for the snowpack. It could be that we had a low snowfall year this year, but the water equivalent is not far behind 1991/92 (another issue for you weather sleuths to dig into).
When I put all this together, I think it's pretty safe to say that the combination of warmth and snowfall for this winter are unprecedented since WWII. It is possible (perhaps even probable) that the current Wasatch snowpack is probably about as low as it has been in mid March since WWII too, but I'd like to see some additional analysis of longer-term snowpack records to see where we stand overall. Again, I appeal to you enterprising sleuths out there to dig into this problem further and provide comment.
PS: I would still take this year over 1976/77 which had very little snow in the early season with most falling late. If you have to pick between snow early and snow late, the former is better. Further, despite the low snowpack, groomers will still fun yesterday. Plus, keep an eye on the storms for Monday-Wednesday. Winter is returning.