I would say no. Some say not under 70. I think the 60s are too cold for them. I think also the older/larger he is the more cold he can stand. I know for sulcatas I've seen baby's need to never be under 80. Everyone has a different opinion. But I would not even think about doing it under 60.
Last fall, I figured if it was too cold for me to go out and lay on the ground in shorts and a t-shirt somewhat comfortably, it was probably too cold for my Russian tort. I have no clue how accurate that is, but it's what I went by, anyway! (I know-- I'm anxious, too-- We just got more snow yesterday though... ho hum... never ending winter this year...)
This winter is just awful! Tomorrow is supposed to be 61 and I'm excited. For 60?! Lol. I can't wait to take my little guy outside just for a few to get real sunlight...
It also depends on the temps on the ground, in the sun, on gravel or basking rocks. My Russian male has a cold frame with a basking light, with outside access.
But the other day, he was outside, in the sun, against a paver. The air temp was 49f. I took my IR thermometer and checked his shell, and it was 79f! It was his choice and he did fine.
And whether your tortoise has a chance to warm up first under the basking light.
A temp gun is really helpful; you can check some ground areas in your yard that catch full sun and see what the temps are down close to the ground, especially if there isn't any wind, as Tom mentions.