Hello Sandy in Virginia, I am thinking about where you live. Okay, Virginia is cold and gets plenty of snow during the wintertime.
But, a JRT will get a pretty good winter coat going on, but you might consider a thermal type dogs coat as well, due to their short coat.
A shelter or dog house would be a MUST, and you can even add heat to them or a good thermal blanket for poochie.
Also, when it gets cold, to the point of freezing, you would have to make sure poochie gets fresh water twice a day.
If on the colder nights (under 30 degrees) I would recommend bringing poochie into the mudroom or a locked kennel area. JRT's are really happier outside, but do like the company of their people sometime during the day.
If your poochie likes being outside I don't see a problem, except during the winter months. I know my girl Ginger would live outside 20 hours out of the 24 if I let her!