It happens. Unless you meet and marry someone through dancing, the chances are that you won't find a partner that enjoys it as much as you.
So, what are your options? Give up dancing? I would say NOT. Go out dancing on Friday or Saturday night, by yourself. That works.
The dance studio I go to (as with most I'm sure) hosts Wed., Fri. and Saturday night dance parties for their students and guests. I'm getting ready to go right now as a matter of fact. The Friday party will have about forty people there with a fairly even split of men vs. women. I will probably dance with 10-12 women during the evening, some married and some not. Some of the married women come alone, while others in the same boat as you, bring their husbands, who sit on the sidelines while their wives dance the night away. I'm sure most of those husbands aren't about to let their pretty wives go out dancing without keeping an eye on them. Then you just hope that they catch the bug sooner or later and start dancing with their wives a little.
Will you get to dance at a party like this? If it's anything like the ones I go to you won't have much chance to sit down. I know that if I try to take a break for a song or two I'll get approached by some lady, which by the way, is quite acceptable in my book. Don't be shy about asking a guy to dance.
So, your question of it being tough to dance solo ... not at all when it comes to the actual dancing part of it. How it affects your husband's psyche and your relationship with him is another story altogether and only the two of you will be able to answer.