I always make my decision based on how much the temp will drop in the next few hours... in AZ, we can have 30 degrees difference between noon and night, so I had some days where it was 75 when I rode, 65 when I was done and cooler at night--therefore no rinse. But, if it's going to stay around 70 for a few hours I think you're fine! Just use a sweat scraper afterwards to remove excess water.
I had a training buddy from Norway--she was a you of I foreign exchange student--who used straw to dry off wet horses with a heavy coat. I suggest a sheet or light blanket, in the stall, until the horse is dry, then a good grooming.
My horses get so much turnout that they usually roll off their heavy coats.
I would say as long as it will still be 70 for a while you should be fine. If you can, graze him out in the sunshine until he is dry rather than putting him in a chilly dark stall. Keep an eye on him as he is drying, and have a cooler at the ready if he starts shivering.
Depends on the barn. My barn is wood, and sometimes, after a heavy Spring workout that leaves my horses really wet, I put them into their stall to dry bc it's warmer. Many barns are not made of metal and it IS colder inside. You need to use discretion.