*edited*

I am seeking info on typical winter weather in southern Arizona and southern New Mexico, see photo. From the data I've seen online, this part of the country I circled is roughly 2,000 to 4,000 feet above sea level, the overall low temps in December & January might range around freezing to maybe the low 40's.

I'm mostly interested in knowing if much snow falls in the higher elevations. I can deal with cool to cold morning temps and rain, just want to avoid snow if possible.

Heat kills me, so Ive never been much of a Desert Rat, though the landscape down there is Awesome.
Temps in the Deserts swing wildly. A 120 degree day can plunge in moments to the low 30s, because there is nothing to retain thermal heat dispersion.

I do know from having family friends that lived in the Gallup area that the region DOES see snow at times.
Perhaps not in recent years but there are photos in the family albums.

Thank you for the input. 

I left out an important word - "winter".  I'm interested in wintering in the area I circled, then slowly meander north towards Montana, Idaho, etc. in the spring - full time RV'ing.

Failed rotator cuff surgeries on both shoulders have caused me to be hyper-sensitive to rapid, substantial barometric pressure changes, which can be nearly debilitating. B.P. here in southern Michigan at 800 feet above sea level ranges 29.40in to 30.50in. B.P. drops roughly one inch per every 1,000ft increase in elevation. I hope to spend time at 2,000ft or higher elevations to see if I get any relief from the pain.

A rapid rise in barometric pressure feels like a blood pressure cuff wrapped around shoulders & biceps, continually pumped tighter. A rapid drop feels like a chemical burn in my biceps, under my skin.

I feel your pain. My surgery 23 years ago took, but time has still taken a toll.

[2015 Z Force 800 53/Trail EPS]

Well, I can say that there are a great many people..some I know and ride with, that winter in that area of AZ as it is stable and warms to around the 70s during the day but is down in the 40 to near freezing at night from about December to about the first parts of Feb. Then it starts up so in March you want to be heading north..IMO. I can't take the heat either. That area in NM is similar but does get colder, has been known for some lighter snows and higher winds at times especially starting in January. A little unpredictable though because it depends on the air flow across then over the Gila NF area. For an example even now in late April its still cool down there and we were headed to the lower parts of the Lincoln NF..which is in your circle, and being around 7000ft its still freezing at night and the highs only mid 60s. The wife said..Nope..so we are delaying a week or so. Now the lower elevations are warming nicely in the 70s +..she might like it but no trees...and no NFs so..F-that

Thank you for input NMK 

The weather all over the planet keeps getting crazier, so historical averages are getting less reliable. I've read articles that predict Michigan climate could eventually be more like the southern U.S. by about 2050. Having lived in MI for 58 years, I can verify it is happening. My need to relocate is for higher elevations / lower atmospheric pressure more than overall weather conditions.

One nice thing about technology is monitoring short term forecasts. If weather is forecast to get really cold / yucky where I might be at, I can look for a more moderate area to head for, since I will be completely mobile. 

I could maybe spend Nov / Dec in New Mexico, then meander west to Arizona for two or three months, then start north, or head back to NM then go north. Whatever I wanna do!

TREES! While I want to experience the full variety of landscapes out west, I'm really drawn to the mountainous terrain of Montana, Idaho, pacific northwest. My only memory of kindergarten / 1st grade is drawing mountains during art time.