What is "early spring" for you? Grants is essentially on the Continental Divide, so it does have winter, snow, and cold weather. A few years ago, I was there in early April and it was cold some days, extremely windy other days (wind closed I-40 at Gallup), and sunny and warm (60s) some days.
However, you have to use NM 117 and 36 from Grants to Quemado just to get to NM 32. All three roads are paved, two-lane state highways, but need repaving in spots. The whole central part of the combined route is on a fairly flat, pretty uninteresting plateau through ranch country. But the north end through the El Malpais Natl. Monument lava flows is geologically fascinating and the south end gets hilly and winding as you near Apache Creek and the Gila Wilderness Area.
If you haven't been there, you should take a side trip when you reach US 60. An hour of so east of NM 36 on US 60 is the Very Large Array, the radiotelescope complex that was featured in the movie "Contact." It is a fascinating, educational stop and has some great photo ops of the antennas.
And, since you are birders, another hour east and just south of Socorro is the Bosque del Apache National Wildlife Refuge, winter home of thousands of sand hill cranes and snow geese and some whooping cranes.