The weather in Ecuador can be very localized and variable in the extreme. At 5000 m. it may be blowing a 60 knot blizzard and in the valley below the sun could be shining on a beautiful day. Fifty miles away in another direction a sub-tropical rain forest will be doing very rain forest things. And an hour later it can have changed totally. What can be said, however, is that there are trends.
Most places have a dry season and a wet season.
Whatever the season, however, the best of the weather in the mountains will be around the full moon. Normally what happens is that whatever the weather pattern is for about three or four days each side of the full moon, the weather will be better than it was. After the full moon it will return to the previous weather pattern. Because of this, and because snow climbing is done at night, plan your mountain climbs around the full moon if you can. The Amazon basin is mainly tropical rain forest so you can expect it to be wet from September to April, temperatures will average around 28 C and it will rain most days, normally in the afternoon.