I don't have any headcanon on this, but I think that Clint and Natasha would maybe not do holidays, because they're working, or those days have bad memories attatched, or they're not into commercialism. On the first point, it's hard to pick certain days in a year to celebrate when you don't know where you're going to be for it, so I think that maybe they have their own kind of holidays or celebrations or rituals, just for them, that don't require a specific day or a bunch of other people celebrating at the same time.

On the other hand, I can absolutely see them trying out holidays, celebrating them when they're undercover because their undercover persona does, and I think there's potential for shenanigans - New Year's Eve at SHIELD anyone?

Two recs that immediately spring to mind:

Clint and Natasha ruin Christmas posted by copperbadge on tumblr (PG) in which Clint and Natasha have a mission at a Christmas market. It has shenanigans! And also a ritual of their own kind of thing - look out for Clint shopping for Coulson. Copperbadge always writes good things, but the dialogue in this is especially fun.

And There Are Deserts Still by Amy on AO3 (Teen and Up, 9310 words, I'd say warning/triggers for personality confusion or aftermath of brainwashing, minor violence). Coulson is Jewish. Natasha attends High Holy Days services with him. Clint bakes muffins. This is a fic about friendship and identity and redemption. It addresses what I said about what holidays undercover personas might celebrate, but takes that a step further. It's smart and induces thinky thoughts.