In general try and stick with the viscosity rating that is recommended such SAE 30 or 40 but you can change the “winter” weight which is a different test/rating for cold crank pressure. An SAE-20 does not equal SAE-20W (different tests). Your engine is temperature regulated with a cooling system so it operates at the same temperature summer or winter so there is no need to change our oils viscosity at operating temperature (which SAE is measured at 100C or 212F which is close to most operating temps) like going from a 30 to a 40 in summer.
To make a long story longer if you require cold weather starting get a good 0W-## or 5W-## oil; you will benefit from it, and as the others said it has to be wet clutch compatible. I run Amsoil in my Polaris (0W-40) because it costs less than Polaris brand synthetic and I get a Group IV oil with a loaded additive package for my dollar.
Hope my rambling helped in some way! 