For a while now I have been walking everywhere when not in combat, it makes the world feel bigger and I feel more connected to my character.

Not all the time, but a good deal of it. I love how the importance of Fatigue in MW (and its decrease with jogging) means that going for a run feels like a potentially risky exertion. It makes me slow down and 'catch my breath' every so often, even if I'm otherwise in a hurry somewhere.

I make my characters run or walk when I think is appropriate for them to do so. I have one rule governing my roleplaying: take only those actions which are appropriate to the character. This rule governs pretty much everything I do in a game. It is my "golden rule" of roleplaying.

Personally I don't think always walking or always running is good roleplaying. Running or walking everywhere we go is not what most of us would do in real life so I don't think we should make our characters do it either.

Generally speaking, my characters walk for a minute or two after a fight (to simulate exhaustion). After that they alternate between running and walking. The percentage of walking-to-running depends on the character's fitness at the time. Most characters walk more often during the early stages of a game and run more often during the later stages of a game. They will walk more often if their health is low and run more often if their health is high. They will walk more often if they are carrying a lot of loot and they will run more often if they are unburdened.

Right now I play my monk-alcoholic character, so I do walk, but with all of my other characters I've ben just running... not very roleplaying but I am fine with it