For winter camping look at Brantley Lake, Caballo Lake, Percha Lake, Leasburg Dam, and Elephant Butte if fishing is one of your goals. Elephant Butte hook up sites are pretty close together but many people dry camp around the lake shore. Caballo has two campgrounds one above the dam and one below and the lower campground is fairly dispersed. Percha Lake and Leasburg are have pretty good spacing in the hook up sites. All of the lakes will be crowded on weekends with pic-nickers but are sparsely used during the week.
If you are looking for weekend only dry camping then there is a lot of BLM land available. Check this link for more info
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