I see this is in the wrong section, will put it in the houseplants sections.

No, you're not in the wrong section - tree ferns can seldom be treated like houseplants for long...certainly not a species like Dicksonia antarctica. And therein lies your problem. Without higher light levels and damper atmosphere, conditions that are virtually impossible to provide in the average home in winter, this Dicksonia will continue to deteriorate. So what realistically can you do? Not much, otherwise I guess you'd already be doing it. Siting the tub in a cooler and damper spot, with an overhead growlight on a 12-16 hour timer, is what's required. Something like a specialist 125 watt fluorescent lamp, suspended from a cellar ceiling in a downward reflector, would be sufficient provided the other conditions are met. The only way of significantly raising humidity indoors under home conditions (assuming you don't have access to a dedicated plantroom) is to enclose the entire tree fern (tub and water dish included) in loose polythene sheeting...but honestly, who's going to do that?!

Any chance of rigging up an overwintering space in a garage or glasshouse instead, and installing lighting and frost-free heating there instead? Can't see any way of overwintering a Dicksonia antarctica trunk indoors under normal houseplant conditions, though.

The photo is indistinct, but your tree fern might very well be the New Zealand variety Dicksonia squarrosa - rather than the Australian D.antarctica. In which case, you have a far better chance of maintaining it indoors as this species is much smaller, both in trunk size and frond length, and it can also withstand slightly lower humidity than its rainforest cousin. It still needs high light levels to thrive indoors, though, and must be kept as wet and humid as possible - none of which will be easy under default houseplant conditions. Mealy bug and scale insect problems inevitably attend indoor Dicksonia squarrosa and require continual vigilance, but unfortunately the available remedies can be as destructive for ferns as the pests themselves!

I have a fern sold as Cyathea cooperi 'Brentwood'. I'm keeping it in my garage by a South window. Temps never really drop below freezing, but then some days in never warms up much either. I've have not been sure how much too water in the cold, and some of the fronds are dying. I don't think I watered enough in a cold December.

Don't know if it will survive. How much abuse can it take? How much does it harm the plant if all the fronds get ruined?

Overwintering a portable frost-tender Cyathea is just about possible in a cool garage - especially if you can bump up the light levels as much as possible. Essentially, you're trying to maintain the fern in a state of near-dormancy, rather than forcing all-year growth. The tub must stay permanently damp, but be careful to go a bit drier if temperatures go really low. When it's particularly mild you need to do the opposite...but don't get caught out with a flooded pot dish and a sudden freeze! It's still a risky procedure, however, and sure to result in a fair ammount of defoliation which can only set the plant back - but it's certainly better than the alternatives of killing the tree fern outdors or dessicating it in the home.