Short answer is 'no' this is a tree and needs to be outdoors - why would you want to anyway?

MG - I'm not so sure mitziecat means Betulla. In her blog she mentions that it grows in a pot on the patio table.
It's not a plant I was familiar with so googled and came up with a begonia type plant. Would this be right mitziecat?

Yes, Betulia can be overwintered in a conservatory/heated greenhouse.

Ah misread the question it seems!

So did I at first and also wondered why someone would want a Betula indoors!

lol Kildermorie a case of us reading what we expected to see!