Some of them do around here. I believe mostly Groffdale Conference but am not sure; and I don’t think they’re the only Mennonites who use buggies.
We have Mennonites ranging from Old Order through Black Car and all the way to people who you wouldn’t know were Mennonite at all if they don’t tell you, because their groups dress like and use the same technology as anybody else.
We also have Amish. If we have any car-owning Amish, I probably didn’t realize they were Amish; the ones I know are horse-and-buggy, no computer, no phone in the house.
It’s my understanding that each new bit of technology is considered by each congregation, which decides whether they think its use will benefit, damage, or be neutral to the community as a whole, and may re-consider their decision later. I’m not at all sure that this isn’t a wiser overall attitude than ‘Hey! New stuff! Let’s all take it up as fast as possible and worry about any negative side effects after they’ve hit us in the head!’ which seems to be what the rest of society is doing.
I know nothing about what’s permitted in sex positions and am not about to ask; but, judging from the size of the families, the Old Order don’t use birth control.