How wet or dry are they? Are the temps cool or warm? How many hours under lights do you give them?

Rexes (and most begonias for that matter) will lose leaves as they grow. After a few weeks they will get used to their new conditions though and start putting on some new leaves if they like their new environment. DO NOT keep the soil soaking wet but also DO NOT let it dry out too much. Both conditions will either put the plant into severe shock and may kill it. If the soil dries out quick, then you may have to water heavy and water more often but if the soil is very slow to dry then you would have to water sparingly (drizzle the surface).

Here are a few of mine a few days ago and they've been indoors for about six weeks.

Thank you for responding so quickly and offering your suggestions. I discovered I WAS over watering them. I was probably assuming same watering schedule as they had been while out just days before. Since I've reduced their watering leaf drop has slowed and seeing new growth on barren stocks. (Stocks which were once full now look like mini-palm trees with only cluster of remaining leaves atop, will they recover from this ordeal?)
Temp is mid-60s to 70s

grow lights 10 hrs/day

humidifiers 5-6 hrs/day

More later, I'll send some pictures I've taken but need to attach. This has been challenging to compose being another first with new phone and all. I've more to convey and will do so when pics are sent. THANK-YOU once again! Bruce

I think you have to kill a few dozen before you learn what it takes to get them through a winter. I still manage to kill a few along the way. One thing is the soil they are planted in. I find a lot of nursery grown plants are grown in a very peaty mix which retains a lot of water. That's great for them, bad for me as I typically overwater and it takes days for the pot to dry out some. I prefer a much faster draining mix so if I watered every day or two, then not a lot of harm is done. It just means more work filling containers and watering chores though.