In my experience they don't bring it up. I think it's because they also prefer no condom and most are on birth control, that combined with being too horny to think straight. It may also to some feel awkward and "ruining the moment" to bring it up. Still it's a game of russian roulette, some women may try to trick you to get a child (it's rare, but not worth the risk). There's no excuse for "ruining the moment", a moment of sex isn't worth the trouble of getting a child with a woman you don't want it with.
My (female) cousin got pregnant because she didn't want to go on birth control and her then (!) boyfriend didn't give a sh!t about condoms. She got twins, yes, two babies at once! What about the guy? Well, he's an a$$hole and the biggest AFC I have ever witnessed, he has to pay child support for the twins and has a restraining order on him. It for sure svcks for him, all of which could be prevented with a piece of rubber.
Then there's the STD's, which you can get even if she's on birth control. If you get one it will svck, who's gonna want to fvck you if you got nasty sh!t on your d!ck? STD's are a great way to ruin your sex life. I don't think the women who doesn't ask really think about this. I can understand it's uncomfortable to ask, but I would get over that discomfort easily by knowing what's at stake.
So use condoms please. Don't stop using them until you're confident the woman in question is free of STD's and is on birth control.