I’m out every day, cold and wet or not!
I work in a very stressful job, supporting people who are severely mentally unwell and often suicidal - and am still doing this over the phone, some days for ten hours at the time, from home (and juggling this around “home school” some days.)
Whenever I am asked, at work, what I do to make sure I still look after my own mental health and as self care, I always say “I get out for walks, especially in the woods as that is the place that instantly clears my head.” I need that outside time now, more than ever, and it is ALLOWED.
There are many people who have exercise as part of a daily routine, and if there are people who have just taken it up now: good for them!
I cannot look after my own family, or continue key work from home, listening and supporting other people, if I am curled up in a ball because my own mental health has gone down the pan 
And I am going out for daily walks and bloody enjoying them. Alas, not to the woods as that is a 15 minute drive and police are stopping people leaving the town I live in.