In the winter you might want to keep the same oil as you may get a lean miss on acceleration if the piston rises too fast, in any event I think the advantage of switching would be barely noticable if at all.
Funny story to tell, first british car, nearly 30 years ago, of course I wanted it to go faster/perform better, I filled the dashpots with WD40, on the thinner oil is better theory as described above.
Ran like poo, would miss terribly when you tried to accellerate. The oil in there does serve a function, I have always heard straight 20 weight, ATF, will work, I have used those, plus the Moss stuff, plus lighweight motor ooil over the years, all worked exactly the same from a seat of the pants driving evaluation, except the above mentioned WD40 of course.