Angela, nobody can predict the weather a month from now. All we can do is look at what the weather has been in the past (see www.weatherbase.com) and then watch the weather forecasts as travel dates approach. It is highly unlikely that all of the snow will remain in a month's time, but who knows? Just watch the weather forecasts and plan accordingly.
What kind of physical disabilities? Italy, even in the sunshine, presents many challenges.
PS: I worry that you've been unnecessarily scared by this week's weather and also my telling you that cobblestones can be slippery.
It is very unlikely you will face snow in March. You will of course need to pack good shoes for the possibility of rain. It is always a good idea to walk carefully in Italy.
Going solo, older, weak legs, have concerns, my shoes are SAS walking shoes, good soles on my boots, and a flash light. I am really not confident nor steady on my feet, so these concerns are real; I am in physical therapy but can't take the therapist with me (lol). I have pretty much decided, if I am uncomfortable, I will be doing taxis in Rome not too concerned when I move onto Florence. I alos have a good hat, gloves, ready to dress in layers. I am trying to think of everything. Any suggestions would be welcomed. You mentioned about the driving rain and the cobblestons so I have work around it. Its nice when you have someone to go with so you can hold onto each other, I don't have that advantage.
Arion's suggesting of a walking stick is excellent. So is your plan to use taxis.
I just took a trip to Rome and I did it with an injured foot. The only times I was nervous was when I was around big groups of tourists, because some times they aren't watching where they are going. They are too busy taking pictures. So be careful around them.
If you carry a cane, I've noticed people get out of your way and give you time to get off a bus, etc. So that is another reason to take a cane or stick with you.
Everybody always needs to watch where they put their feet in Italy when they walk. That's how I injured my foot: Looking at the sunset while I was walking. I put my foot in a pot-hole.
You will see plenty of Roman ladies taking their time when they walk down the street, so you will feel at home. Sounds like you are packing very intelligently, and you are right that flat Florence doesn't have as many challenges -- but still, don't walk and gawk at the same time!