You can cut most begonias back but it would be nice to know which one you are talking about. If you prune it back too hard it might kill it but if you take say half of it then it should be fine. Propagate the pruned tops if you want to have some for backup or give away.

I take it you took indoors an annual 'wax begonia'...not a tuberous variety.
I know they are kept going as long as they can, somewhat like the impatiens, and sooner or later when the low sun of winter doesn't support them well enough, they wither and die.
You brought yours along and the lankiness suggests they did not receive adequate light.

So now what to do. Cut them back to soil level and give them new potting soil in a clean pot and give them a good window --south or west or east--and let them come along.

But since they are annuals, and they cost so little, maybe you would rather buy new plants and trust they do for your garden what the old might not do again.