It depends what kind it is and what situation you have it in. Unfortunately Mark Longley's website http://www.thefernhouse.moonfruit.com/ which used to explains all you need to know about growing tree ferns in Britain, doesn't have that bit any more, probably because he's moved to New Zealand.

One crucial factor is precisely what species have you got. If you have a Dicksonia antarctica, D. fibrosa, D. sellowana, Cyathea australis, or C. smithii, then they are really quite hardy and can survive out of doors, even in the ground, indeed better in the ground, in many places in Britain, provided they well watered, not waterlogged, and the growing tip isn't killed. (Though unfortunately most of what is sold as C. australis is really C. cooperi, which isn't so hardy; also D sellowana in cultivation is almost as rare as rockinghorse shit).

These conditions are available in the milder parts of Britain, especially inside urban heat islands in the south and west of the country. Tree ferns growing out of doors are common in places like London, Portsmouth, Cardiff, etc. Having overhead shade, to reduce radiational frost on clear nights, is a valuable assistance in keeping them alive in many locations, though in fact Longley's former garden in Southampton where he had all of the above did not have that shade. In fact the main problem with keeping some of them alive in Britain, especially the hardiest Cyatheas, is that it gets too hot and dry in the summer, though they would have loved it this year.

The ones surviving out of doors in britain are mostly D Antarctica, since DA is one of the most frost hardy (but not the most, contrary to what most garden centres say) but also, and this is the crucially important thing for Britain, the most drought hardy of the above five. It also survives being transported barerooted, indeed having its below-ground parts roots cut off, unlike any of the others, which has been a factor encouraging its transport. But it is a lot, lot slower growing than the other times, increasing its trunk at about an inch a year, whereas other types can produce a serious sized trunk within a decade. It seems likely that you can give them suitable conditions in Bristol, if you are in the urban heat island and not high up some hill or in a frost pocket.

Curiously, the thing that does sometimes kill them in a pot in winter is drought, if the pot gets frozen on the top and can't transport water. If the pot is frozen or blocked at the base, waterlogging is also a possible winter problem if the pot can't drain. Sometimes the winter protection they are sometimes given, eg wrapping the whole plant, can also kill them, because they can't breathe. Get condensation inside, goes rotten.

They will not survive if the growing tip is killed, so it is common to make doubly sure by protect that, eg, by putting some straw in the crown. Though this needs checking to make sure it doesn't get waterlogged, may need changing. A small plant in a small pot also risks getting frozen through.

But given that it is in a pot, and it is fairly small and you can move it, why take the risk? But if you haven't got a suitable indoor location there are often good places outside you can move a pot to. Right against a wall gives a lot of protection, reduces the amount of sky visible to reduce radiational frost, head stored in the wall in the day given out at night, some heat loss from inside the building also. For example, I have a Protea cynaroides in a large pot, which is only rated down to -5C. I have kept it outside through several winters, in the Chilterns, without fleece, despite several frosts rated down to -7C. How? By moving the pot hard up against my patio doors during the at risk period, roughly November to April.