Taking Outside to Recieve Rain water?

Would this hurt my girls?

It's a pretty big difference temperature wise...
But Rain water is the best...

I was just gonna carry them outside, (5 ft. away from grow room)
Suns not out... it's pretty rainy right now... and I dont think my tap water is doing them much good... (I Use a water softner for my water (bad?), but I also let the water sit 2 days before using...)

I'm just wondering if my girls would be ok taking them outside...

I don't think this would hurt, but it also wouldn't hurt to invest in a PH meter to test your water before giving it to your plants.