Are there any means to get items that are awarded by past seasonal events loot boxes? When purchasing a loot box, is there an option to select boxes from a specific seasonal event, or are they always from the current event, if any?
As per this article from Polygon back with the summer events, and personal experience, the answer in short is no.
The boxes are for a specific time/week, and the items are only available during that week as well. You also cannot save up loot boxes in hopes of them becoming the seasonal ones when an event begins, since box items are determined when you earn them. You can only earn them during that week from leveling up, freebies, or arcade.
You also do not get the option to select which box. If it is an event with special loot boxes, every one you would normally earn will give you a box from that event, you don't get an option between them and normal ones.
Boxes are meant to be rare and for limited times. While we won't know if events will reoccur yet since we haven't done a year loop, it seems likely they will. However there is likely to be new stuff for those boxes which may or may not include stuff from the prior year.
Quote from Kaplan:
"We wanted the seasonal loot boxes to feel more rare and special and the items within them to feel more rare and special," Kaplan explained in a developer update video about the Summer Games event uploaded yesterday. "For that reason they’ll only be available for the next few weeks and you won’t be able to buy them for credits either."
And as an amendment, this question was already slightly touched upon in Arqade before.