When should I plant them and what to do with them while waiting for that season to come?
Are these seeds from your own trees that go through their routine annual cycle? If from your own yard, deliberately planting them seems redundant since you should be finding many transplantable sprouts here and there throughout the spring and summer from past seed drop. I've gotten some very nice sugar maple saplings that way.
Some considerations when planting trees from seed. Collect seed when it is mature. A good indicator of maturity is when the seed is naturally falling from the trees. Most trees mature in the fall. A few trees (elms, silver maple, red maple, cotton and willows) produce seed in the spring or early summer.
Then it all gets more complicated. There is quite a bit of university extension service info on the internet regarding planting trees from seed. You might get a good and quick answer over on the Trees Forum or the Maples Forum too.