I have been to a ton of places with the family. I didn't pay attention if you will drive or fly and where you live. If you are flying, I suggest Utah, cheaper, usually better snow, cheaper accomodations, slightly higher cost of flights
Alta - no snow boards and plenty of greens now
Brighton - very beginner friendly and most days goes 9am - 9 PM, you can ski from top to bottom on Greens.
Solitude - fairly beginner friendly, but I would just keep driving 10 minutes up the road to Brighton
The other side of the range in Utah is Deer Valley, Park City etc. They will be more $$$ and the snow will typically not be very good at that time. Deer Valley I think is still no snow boards.
On the same path and next to Alta is Snowbird. The terrain is steep, so I would not go there unless you are experienced skiers. I like it alot, but I always end up with some less experienced skiers and they hate it there.
Utah has lots of other family friendly places like snow tubing, snowmobiling and sledding hills
If you are set on Colorado, my ranking for families
Copper Mountain - The green runs are plentiful and they are separated from the blues and blacks
Breckenridge - already mentioned, I rate then below Copper but good
Beaver Creek - expensive but lots of wide open well groomed greens and easy blues
If I drive my default is
Wolf Creek Colorado, low cost and best and most snow in Colorado and it's not even close. Stay in Pagosa Springs, the only concern is the road up there if you don't have 4x4. 95% of the time there is no issues, but because they get the most snow, it can get like 2 feet in one day. Very family friendly. Issue is, this is pretty much a place to drive to, it's way away from any civilized airport. No frills kind of a place. Lot's of tree skiing if you like that like me and my family.
The other area in Colorado that is nice is the Aspen area. $$$
Buttermilk is almost all green and super beginner friendly
Snowmass has tons of greens but it is a giant place
During that time, summit county Copper and Breckenridge will be very crowded
I have been to New Mexico. Ski Apache, Taos, Angel Fire, Red River. Red River is super nice for beginners. The issue will be big crowds and iffy snow conditions in all the NM resorts. IMHO Taos is far the nicest in New Mexico but I didn't think very beginner friendly.
So if it were me, I would go Utah (Brighton and Alta) or Wolf Creek in Colorado.