If you are planning an expensive marketing and advertising launch, then I can see wanting to wait for the best possible timing.
But if your launch is fairly modest, then why wait? T-shirts are pretty standard and can be worn year round. And since they are non-perishable, there is no risk in them going bad. If you sell through your inventory during the Fall/Winter season, you can always re-launch with new designs for the Spring/Summer. If you don't sell through, just continue to sell the same inventory during the next season.
Another option would be to start by launching with long sleeve t-shirts, thermals or hoodies. But make sure you can sell through, otherwise you will still have them in stock and need to spend more money on t-shirts for the Spring.
This is all based on selling directly to the consumer. If you are planning to launch by selling to retailers, then now is the time to sell to them for Spring/Summer. Typically, buyers purchase in the Fall for February delivery to have on the shelf for Spring.