I live where it snows....ask me anything:)
I’ve compared heartrate and effort on many runs. I’ve spent winters almost exclusively on the treadmill and other winters where we have no snow...running outside mostly.
My findings are .....that it is wash. I think I get a slightly better workout on the treadmill. I tend to go a bit longer or harder on the treadmill. I do most of my running at 3-8% grade and go off a heartrate mainly I don’t pay to much attention to the speed or grade. I just adjust as needed to keep the effort approximate.
I do some of my repeats at 0% and some at 15%. If it feels to easy I go faster or steeper...if it feels to hard I back off a bit.
I have run a few marathons off of mainly treadmill and a few exclusively on the roads. My results are identical. Neither seems to help or hurt.
I do find I recover faster from the treadmill. My normal 10 mile run at 6:30-7 per mile is about an 8 minute mile at 6% . I run for 70 minutes and ignore distance on the treadmill.