I have a Motobecane café latte disc hybrid bike with thin road bike tires. I was wondering if it's possible to switch to for dirt tires for trail riding?

Not ideal, but worth a shot. The Caffe Latte looks more like bike build for roads than one purpose built for trails. But, it really depends on what sort of riding you have in mind. Groomed trails, or single track? If the latter, then probably best to consider a mountain bike. If the former, then it could work.

you could probably fit 700x32 or maybe x35 cyclocross tires on there, depending on how much frame clearance there is with the x28's that bike came with.... good cross tires are expensive and wear out fast on the pavement.

i ride on hard pack and gravel dirt roads and trails all the time with 700x32 road tires on a hybrid. knobbies are only needed on soft surfaces like sand, mud.

Thanks for the answers.

I'm more likely to do more groomed trails. Would the tires itself work?

Another question I have: Since I'm planning on riding in the streets of San Francisco during the winter, should I switch out my tires for something with more grip on the road? This bike has disk brakes if that helps.

suggestion: Vittoria Voyager Hyper in 700x32 or 700x35. these are excellent all around hybrid tires.. I'm using the Randonneur Hyper x32 from a few years ago, whcih si the same tire (they changed stuff up some). these do great on smooth hard pack and gravel. this is a 120 thread/inch tire, that has that magic carpet ride of a really good tire, its got the vittoria version of puncture protection. run them around 60-70psi on the dirt, and 80 on the road.