I put mine outside last year at 5.5 weeks. Had to or choke to death on the dust. I had 22 of them and they were creating a huge mess. First two nights they had supplemental heat via a heat lamp. After all, the temp inside the coop was 20 degrees and they were just babies. Every time I checked on them they were sleeping in puddle by the pop door - not even near the heat lamp. So I took it out. No point risking a fire if they weren't even going to use it. That was on April 1st. We continued getting snow until June 6th.
This year I brooded mine outside in the run from the start - the run, not the coop - and it worked way better than I even hoped. They were all strong, healthy, and active. I use a heating pad and a cave rather than a heat lamp. Temps were in the teens and twenties, yet they spent most of their time running around in their pen, exploring and growing just as they would have under a broody hen. I'll never brood chicks indoors again! I've now raised 3 groups of chicks this way.
Chicks do need a lot of care, but they aren't the delicate little divas we sometimes try to make them out to be. Broody hens raise chicks in the cold just fine and they don't need any help from us to keep them warm. Chicks scoot under for a quick warm-up and then they're back out running around learning to be chickens.
Yours should be fine!