I do sometimes but I usually carry my phone. Sometimes for music, sometimes just got emergencies.
There's not a lot of good walking weather in my area though. So it isn't common for me. Spring and Fall are fairly short now, and summer/winter is usually too hot.
What kind of climate do you live in? I'm curious what area you're in where the outdoors is too unforgiving. I love walking on doors in any kind of weather, although I understand if it's prohibitively hot and cold someone wouldn't want to walk in that kind of weather. I often keep my phone on me too, but I find myself so distracted by nature and the change of scenery in general that I don't even think to look at it. It's pretty easy for me to disconnect for hours at a time, if not just to make sure that my family hasn't messaged me for something important.
You can probably infer the climate from my instance name.
Canada.
This year, winter has been pretty unpredictable. We had a bout of 10C weather, bookended by snowfall both before and after, all within about two weeks.... The rest of the season has been equally unusual. Summer last year went into the 30C range, far too warm too be comfortable outside no matter what you're wearing.
Most winters are well below freezing. This year was very strange.
Spring and Fall are usually nice walking weather, but the last few years it seems like both spring and Fall temperatures have been a "blink and you'll miss it" kind of deal. It sticks around for maybe two weeks then straight into summer/winter.
Global climate change is really screwing with my ability to enjoy the outdoors.