I've just renovated my freezing bathroom. I've very pleased to say its no longer like showering in a walk in fridge! It depends how much you want to change what's already there, but things that helped were:
Taking some of the tiles off and putting water resistant MDF tongue and groove panelling in- wood is so much more insulating.
Putting underfloor heating in. If that isn't viable, could you perhaps change the tiled floor for a lino (I think it can go over the top of existing tiles?) They look so much better these days, are cheap and quick to fit, and its so much warmer under foot.
I put a huge heated towel rail in, way larger than it needed to be in terms of the BTU rating. They really seem to vary hugely in terms of the heat output, so read the small print carefully, and get the one with the highest heat output that you can fit in the space. I got one from Screwfix, and its brilliant. I also read that white ones are more efficient than chrome ones, so I've got a white one. I've no idea why, but it does seem to make a difference! I was worried it wouldn't be enough, but I didn't have room for a radiator as well, and luckily its been absolutely fine. I also fitted a shaker style peg rail, and unless I actually want a towel to be warmed up the towels hang from the peg rail rather than sit on the towel rail.
There were loads of drafts coming in around the bath, so the fitter packed out all the gaps with insulation, this has made a huge difference. I also specifically got a bath that is particularly good for keeping the heat in, but that was quite spendy.
Finally, fit a waterproof, thermal roller blind, and pull it down as soon as it gets to dusk- it makes a surprising difference.