I just got off the phone with the folks at Taos Tactical. He referred me once again to handgunlaw.us, which has the alphabet soup of statutes and prohibited places. He reaffirmed that Texas and NM are very similar in what is and is not permitted, and that as a TX CHL holder, I don't have to put my unloaded gun in a lockbox while traveling through, but can leave it strapped on.
As for ski areas, they are not state parks, but most are in a National Forest. As such they are legal for carry if you have a CHL, depending on state law. The guy I spoke with is in the Taos Ski Valley and he carries every day at the ski areas.
The pertinent regulations I found were on the Monongahela NF website (of all places!). A link to the PDF is on this page:
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Laws Regarding Firearms on National Forest Lands
First, the primary laws governing possession of firearms and other weapons on National
Forest are State Laws. These laws were developed by the states following establishment
of our Cooperative Wildlife Management Agreements. Most notable of the state laws
concerns controlling firearms on the National Forest are “cased gun laws”.
Cased Gun Laws: As the name implies, this law requires that all firearms on National
Forest be unloaded and kept in a case. Virginia and West Virginia have similar “cased
gun laws”. In order to allow hunting, these laws make an exception.
• It is legal to have loaded firearms on National Forest during the authorized
general firearms and muzzle loading gun seasons for bear, deer, grouse, pheasant,
quail, rabbit, raccoon, squirrel, turkey, or waterfowl. This exception is very
specific and applies only during the period when it is legal to take these listed
species and doesn’t include carrying the loaded weapons in a vehicle.
• Because hunting on Sunday is prohibited, carrying a loaded gun on National
Forest is not legal on Sunday even if it is the Sunday in the middle of the general
firearms deer season.
• The second exception to this law allows people with a concealed weapon permit
to carry a loaded, concealed, handgun either on their person or in their vehicle
while on National Forest. This does not apply if the person is engaged in a
primitive weapons season or chase only season.
• People muzzle loading or bow hunting may carry a concealed weapon as long as
they possess a concealed weapon permit.
Now, I just have to find a snow-proof holster!