It's an old fashioned phrase but "cut your cloth accordingly" strikes me as the way to deal with present giving when times are tight.
I was lucky enough to have only a very few years when the dcs were small and I wasn't earning. However, during those years, while we didn't always have a joint account, presents for family were bought out of joint income with ex-h (who earnt more at the time) contributing more. It was never a question of either one of us having to bear the lion's share regardless of whether we actually had the money to do so.
Now, happily unmarried to dp, we have a similar system in that while we don't work on a "your money is my money" principle, we always share the costs but don't necessarily worry about proportionality. Again, it depends who is most (or least!) flush at the time.
I love to give carefully chosen, thoughtful presents but it can be a weight off everyone's mind if there's a sensible understanding about the level of giving. Nobody in our extended family wants anyone to go into debt when actually, it really is the thought that counts, not the magnificence.
So rather than denying all gifts, just say that you'll be keeping things small and simple this year. People honestly don't mind.
But for sure, you need to talk to your husband about a greater degree of financial equality.