That first one is Mammillaria pringlei, now M. rhodantha ssp pringlei to give it its full name. Definitely not hardy outdoors for you.

The second one I'm not sure. It looks like a Mammillaria but the shortage of spines on top make me think it might be a Rebutia. Rebutias tend to have somewhat, or very, rectangular to oval areoles, while Mammillarias have quite round areoles. Also, flowers appear from right at the base of a Rebutia. If a Rebutia, it may be quite hardy, but probably not quite hardy enough to stay outside.

Both Mammillarias (most of them) and Rebutias (all of them) flower best when they have a cool (or cold) winter rest. Rebutias in particular need to stay pretty cold for a while, Mammillarias are usually OK even on a window sill allowed to get cool just at nights. You may be able to keep the plants in good healthy growth in your warm sunny room, but they may still etiolate, especially if they stay warm at night. But will you get any flowers or not next year? Both species will be perfectly happy to stay dormant at around 40F-50F. Both will be able to take some frost even if they are kept dry. Maybe you want to keep them cool for two or three months right in the middle of winter.