It really depends for me. I use bandanas to cover my face or head, wipe sweat, tears, ect but I don't usually blow my nose on em and I keep the ones used on my nose separate from those I wipe my face with. It's not a sanitation thing that keeps me from straight up blowing my nose on hankies, it just grosses me out a little too much. The one exception is when I'm going to be outdoors long
enough that tissue won't cut it. This is rare though, If I'm outside that long it's usually warm and I don't get colds in warm weather often (nor do I go out hiking, ect when I'm sick).
As far as the sanitation issue goes; if you are sick, neither a tissue nor a hankie is particularly sanitary. No matter which way you look at it you are still holding something in your hand and blowing mucus into it. When you're sick you're suppose to wash your hands often, no matter what you're blowing your nose with. The issue is less tissue v.s. hankie and more about whether or not you're washing your hands often enough. If you have anything worse than a cold you probably shouldn't be around people anyway (but let's face it, it's gonna happen). I'm a super stickler for sanitation but this issue doesn't particularly bother me.