Apparently I don't know how to upload photos on here....

Normally I would say wait till spring, but I think this guy needs help asap. You wait till spring you may have a shriveled cactus. How did the roots look?

Ok now I'm curious if the bottom half is dry I mean dead dry. Like no more life left. If the bottom part is dead you need to turn it into a cutting. The bottom looks desiccated. I don't think the roots are working much if at all. Sometimes with cactus if not watered during their growing season and when it's hot out the roots will dry up and turn to dust. I've had this happen a couple times. If not getting water they will just shut down. It takes a long time for them to die this way, but even cactus will eventually die without water:(.

If that lower third of the cactus looks and feels alive. Start giving it little sips of water about once a week. It probably feels like you should dump water on it, but the cactus can't absorb that water due to the lack of roots. So the little sips will jump start it. Keep it warm and in your brightest window.

Your soil needs to be amended. Looks very water retentive. Get some perlite and or pumice. Do a mix of 60% perlite and or pumice, 40% cactus mix. Get a small terra cotta pot. The pot it's in is too big and will just complicate things. A pot that's 4 inches wide would be fine. Terra cotta will usually always have a drainage hole, and allows moisture to evaporate. Rinse and strain the perlite and pumice with an old kitchen strainer:).

If the bottom is desiccated cut the bottom third off. If the flesh looks healthy not brown or dry spots stop cutting, but if the flesh is bad keep cutting up till you see healthy flesh:). Let the cutting callus over for a couple weeks in a room that's bright, dry, and warm. No direct sun till roots form. No water till roots form. They don't have roots so they can't absorb water. Once a callus has formed over the cut set on top of the mix, and wait. Roots can take awhile on cactus. Don't be alarmed if a month goes by and no roots form. It's not the growing season so it may take two or more months. Don't go checking every week they won't be there. Slows down the process when constantly lifting and checking. Plus a side note. One time I was checking a cactus cutting for roots and it finally had them. I was a little to rough while checking and they all ripped off. So that set me months back:(.

All of a sudden your cactus will perk up. Then begin to water. You will know it's pretty noticeable on cactus because they will plump up when the roots start searching for water;).

Goodluck:). If you have any questions just ask.

Your other cactus looks like pics I've seen where cactus have red spider mite damage. I've never had it. I would keep that guy away from other plants.

Thanks for the advice - the soil is whatever he had it in, but we've transplanted several others into soil that's 50/50 soil and sand. Would that work? We normally keep perlite on hand but have been out for a month or so and every place we've stopped locally is out for the season.

Also - if I cut it at soil level and keep going up til I find (hopefully) healthy flesh, so I take the cutting and put it in the soil to callus up or leave it bare until the callus forms and then put it in soil? If I'm understanding you right, I'd be transplanting the top portion of the cactus, not the root part, right?

Thanks!

And would rooting hormone be of any use for this process? I used that on some other succulents of his that we are working on and it did well for them.

Looks dead to me. But cactus, like people, do not live forever.