I agree that this is not the ideal time-of-year for working "Al-Fresco", but as the car is stored in damp conditions, Chris T's point is all-the-more valid. Brake fluid suffers the same hygroscopic effects of course. In the case of brake fluid, it does not get hot and release water (as steam!!) until you are braking hard, perhaps at the bottom of a long hill or downramp from and elevated Motorway?? Not a good place to realise that you should have changed fluids earlier!
I changed gearbox oil on my 20-year-old TF and the previously difficult 3rd to 4th, and 5th back down to 4th gearchanges became smooth-as-silk.
My gearbox oil was not low (I measured the volume which drained-out), but the old oil was pretty dark in colour:
View attachment 138944
Changing the oil was an easy DIY job: a longish drive to get the oil hot, raise rear wheels on axle stands or ramps, remove drain plug (3/8" square socket driver fits nicely), then leave to drain into a 4-pint empty milk bottle or similar and go and have lunch.
Re-filling is a slow job unless you have a pump. I used a length of plastic tube and funnel from above:
View attachment 138945
Whilst underneath the gearbox, worth checking that the gaiters around the cables are not like mine used to be:
View attachment 138946
Again, it was an easy DIY job to change these.
Happy motoring next Spring!