I run frequently and have arthritis in my toes and what has felt like the start of it in my hands for several years, but I im too beligerant (aka stupid) to accept what hasn't become painful.
Usual rule i go by in the cold it try increasing pace a bit early in the run or do a bit of warming up before leaving the house.
The areas I work to keep warm are hands and feet, areas where circulation is often weakest in the cold. The back of the neck is a good one if you tend to feel the cold a lot and there are neck tubes ideal for this, personally I hate them but am the weird exception so get one. Water will have frozen before I move from shorts to leggings but if your arthritis is in the knees or hips make this shift early, even try some wicking base layers underneath them, these are fairly cheap.
Waterproof gear is the hard one, as having insulating clothing alone is worse than nothing if it gets wet. My preference is to go for the lightest weight gear with vents under arms etc. I find that the breathable stuff is not as waterproof or too thick and makes me sweat more, I do sweat a lot, so accept the inevitable sweta inside to escape the few vents and just make sure I get out of the wet gear as soon as I get home before it goes cold. If you don't sweat lie a firehose the more high tech breathable gear will likely work well for you.
One trick I have known work for some who run in cold weather and only need specific joints protected from the cold not the whole body is tubigrip support bandage, choosing the largest size that stays in place to provide localised heat without un-needed support.
All of these may be useless for you, but they are observations I have made many from the days when running gear was a bit more basic than now.