Hi, J..
My 19 month old son rejected his crib very early on and was sleeping on our queen size bed between my husband and me. This recently became a problem and I knew we had to get him into his own bed, in his own room. We also have a very small house and are saving for a bigger one, so I needed a solution that would grow with us. I bought a twin size trundle bed. I pull the bottom mattress out and my son sleeps there. I don't have to worry about him falling off the bed because I don't pull the mattress up, he is only 8 inches off the floor. During the day the bottom mattress rolls under the top and we have one twin size bed and room to play. This was the best thing I ever did. We are all sleeping well and my son loves his new big boy bed.
Oh, BTW, I chose a trundle instead of just a twin mattress on the floor so we would have the extra twin bed for over night guests.
So to answer your question, if you are comfortable with the arrangement, I would say a three year old would be just fine either in a toddler bed or a twin size bed.
Good luck,
R.