Some herbs, like basil, are annuals and have a built in lifespan and are done at the end of the season. Oregano and thyme are perennials. Where I recently moved from in zone 6 in Ohio, they over-winter in the ground. They go dormant in the winter, and start growing again in early spring.
Where you are, they aren't likely to survive winter outdoors, especially not in a container. But yes, you can bring your container of perennial herbs in for the winter, if you have a good spot for it. You need to do a reverse hardening off. A couple weeks before you might expect frost, move your container from its (presumably) full sun location to a shadier spot to help it adapt to life indoors. Then bring it in and put it in front of your brightest, sunniest south facing window. If you don't have a space like that, then it will probably need supplemental lighting, which would be a dedicated lamp shining directly on it from just a few inches away.
Understand that bringing them in isn't really so that you can use them all winter. Mainly it is to keep them alive so that they will have a head start next year and get even bigger. They are not going to grow a whole lot indoors in winter. Don't fertilize them (starting now!) and don't give them as much water as they have been getting - plants that are not growing much are not taking up much water. So watering amount that was appropriate, will now be over-watering and could lead to root rot.
The fact that they keep blooming suggests to me that you aren't cutting them back enough. You don't want to just "snip the blooms off," you want to keep cutting the plant well back, cutting off a third of the stem. Before you bring it in, cut it back hard, maybe half of the length of the stems. Oregano and thyme that aren't cut back regularly will turn hard and woody at the bottom and will not produce from the woody areas. If it has already gotten woody at the bottom, don't cut into that. It will not grow back from any woody stem you cut in to.