What a sad problem.
I am wondering if you refer to intimacy as being 'pawed over' because in the last 20 years, your husband has not given you the care and attention in bed to make sure you got as much pleasure from sex as he does.
Remember The Hite Report many years ago? A huge proportion of married women spent their lives pretending they enjoyed sex because they felt they had to, or it was their duty, or that their husbands would leave them if they did not 'submit'.
Men usually connect a woman's willingness to have sex, with their own sexual attractiveness.
He probably sees your rejection of sex as rejection of him in some way.
Some women have genuinely low libidos and whatever attentions they receive, sex is still a chore because they simply cannot get aroused, or it takes longer than the man is prepared to spend.
And many men are just selfish and don't care, once they have been satisfied.
Whatever the reason, and in spite of the 'moods' (what about your feelings?) you cannot spend the rest of your married life resenting your husband and possibly feeling obliged to go along with his urges, can you?
Would you be bothered if he found sex elsewhere? Would he be happy with that - or does he just want you?
Only you know the answers to such sensitive questions.
But as others have said, you are under no obligation to have sex when you don't want to and you simply must make this clear to your husband, moods or not.
Mumofmadboys asks a valid question, and if your reluctance is recent, that could be the cause.
I have a feeling, from what you say, that sex has never been particularly enjoyable.
If this is so - 20 years is a long time to put up with such an intimate and (to you) distasteful task. Now you deserve to be heard and respected.
If you had a medical problem which precluded sex - he would have to accept it, wouldn't he?