The ones that you can store over the winter to slowly ripen are called “long keepers”.

Just as an FYI, simce they are picked fairly green to ripen indoors, they will never have that summer-fresh taste. However, they are still a bit better than the plastic-tasting tomatoes you see in the grocery store in Winter!

If you’re talking, however, about keeping the cherry tomatoes indoors (on the plant in a container under lights” over the winter), you might be able to. However, if you want to do that, you may just want to grow them indoors from the beginning, starting the seeds about this time of year.