An open umbrella with a wheelchair or
ECV is
dangerous. Not only is there a stability issue, but it will often be at eye level for many people walking nearby.
Don't agree with it being a safety issue. It can be, but that doesn't mean it
is. It all comes down to the combination of the person, their abilities, the aid they use, the umbrella used, how crowded the area is etc. etc.
For instance a person that isn't used to using an ECV, rents one and then uses a huge umbrella, on NewYears Eve in MK, perhaps also having some muscle strength problems; huge risk of ouch.

Taking away 1 hand from mastering an aid they aren't familiar with, that -depending on the type- already is proun to tipping over, is at eyelevel heigth for many folks, huge umbrella meaning high chance of not being able to oversee all of the area covered etc. Accident waiting to happen.
But does that make it always an accident waiting to happen? Do not agree.
I am a powerchair user, know my chair inside and out. Kinda know the disney crowd also by now and their 'let's jump in front' and 'the disney wow, stop dead in your tracks'. My chair is a high one. I use a small umbrella that basically means I can keep my torso and backrest on the bodyside dry. If I aim just right, I can even keep most of my seatpillow dry, but don't bother with that really as I've always got more covers with me. (living in rainy country makes you prepared). I can only use one arm for mastering my chair to begin with, so using my other arm for something doesn't take away from that. My umbrella has to cover my headrest to keep me dry. The top of that headrest in combo with umbrella now means the umbrella is at the same heigth of the average male. Read; as far as height goes I'm in there with all the other walking umbrella female users. My umbrella doesn't stick out of the chair. Folks will actually first hit my wheels, footrest (ouch for their shins) or side of the chair. No risk of poking any eyes unless you do really really weird things.
So many folks, so many abilities, so many aids, so many factors that in total will make up the picture that in the end results in it being safe or not.
As for the opening question; mostly answered that one. I use a pocket umbrella, as it keeps my head, torso and backrest (side I lean against) dry. I hate using a ponso or raingear. Reminds me too much of all of those days riding a bike to school, 10 miles to and fro, getting rained out about 60% of the time having the lovely choice of being wet from rain or from sweat of the rain gear. Never mind how 'good' a quality they are or not. I'ld rather have a little wet lower leg. I'll dry that off, put on a new sleeve on my footpillow, dry of my teva slippers, if need be put on a new seatcover as my chair only has cotton on it (skin can't deal with any other fabrics like those that are not absorbing fluids). I could also change my backrest sleeve, but that's more work so don't really like it. Besides, I don't like a wet head or torso and don't mind holding a small lightweight umbrella since my chair actually helps me keep it up so it doesn't cost me any real strength.
In Florida I cover my joystick up with a raincap for the hair. Just a making sure the "it can't happen, but does happen" doesn't happen while I'm on a trip with the rain somehow causing a short circuit and me being stuck. It shouldn't be possible to begin with and at home I NEVER cover it up. It gets loads of rain, including those pour downs, yet still I find myself covering it up in Florida as if to say "I'm not going to jinx myself any more than need be". I think Animal doesn't like it though. I've got an Animal (Muppets) antennatopper as my joystick. After that raincap he looks like he's had a nice clean old-ladies haircut. He seems to look a lot grumpier at those moments.

Even gets comments from little kids he looks weird like that.

Sure, when rained on he looks like a drowned cat but he can work that look like nobody can.
