Your vientos are opposite of what they should be. That's why the precipitations are also off.

In the first cell (broadly between equator and 30° N) the air RISES at equator. It then travels northwards in HIGH ALTITUDE and sinks around 30° N. To close the loop it then travels on ground towards SW (the Coriolis force deviates it to W). So the winds between 0 and 30 go from NE to SW while you did them from SE to NW. I remember your map and I think I told you that around 30° N just north of the huge mountain range you will have a mother of all deserts.

In the second cell (broadly from 30° to 60°) the air rises at 60° (because of adiabatic expansion, it creates precipitation) and travels in high altitude southwards towards the boundary with the first cell. There it sinks and to close the loop travels back on ground to the NE (Coriolis here deviates to E).
So the dominating winds between 30 and 60 are from SW to NE while you did them from NW to SE.

For more details about atmospheric circulation click on the tutorial in my signature.

To the question Winter/summer.
Why would you want to do that ?
But if you wanted really to do it then there are basically only 2 seasonal large scale features to consider.

1) The first cell doesn't rise exactly at equator. It rises at a line called ITCZ. And ITCZ oscillates between a position N of equator in summer and S of equator in winter (seasons are here considered in the norther hemisphere).
So your winter and summer maps would have different ITCZ positions from where follow precipitation and temperature.

2) Monsoon like oscillations. These happen around tropics when a very large land mass borders a very large water mass. In summer air rises over hot land and sinks over cold ocean. From that follows a very humid airflow from ocean to land and the adiabatic expansion over land creates huge precipitations.
In winter the cycle reverses because oceans' températures vary little while land cools massively down. The air then rises over ocean and sinks over land. Consequence are very dry winters.

Btw your map is still very nice.