Alot of people are totally idiots when it comes to octane and just what it means.
High octane, all else being equal, will make your saw start HARDER in the winter.
Think about just what octane is.
Octane is the gasoline's resistance to detonation.
that means higher octane....means harder to detonate.....and burns slower.
Remember, it used to be they put lead in gasoline to make it higher octane. You think that lead magically made the gasoline soooo much more powerful like many people magically think? NOT.
High comressions need high octane so the gas doesnt ignite TOO EARLY.
On modern cars that require high octane, the computer can compensate by pulling timing (less power) if you run too low octane. Thus there "seems" to be a big performance increase going to a higher octane. But in reality, you are just running the correct octane to get full timing advance.
Run the octane rating that is called for. Anything above that (again all things being equal), is a total waste of money regardless of what BS anyone tries to sell you on.
I hate the "regular" "MID" and "premium" nomenclature on the pumps. Got too many people brainwashed into thinking "premium" somehow means better. Would people still have this opinion if instead of calling it "premium" they called it "we loaded this fuel with a bunch of stuff to make it burn slower"
Now when I say "all things being equal" earlier......ethanol is a game changer.
Around me.....all grades have the same ethanol content. Unless you specifically seek out a station that sells E-free and charges $1.50 MORE per gallon for it. But I'd imagine there are still some places where 87 octane has the 10% or whatever ethanol, mid is a little less, and premium little to no ethanol. If this is indeed the case, then by all means get the premium
Oh, and to answer the second part of your question about motor damage....
Well, you tell me. You really think a harder to ignite, and slower burning fuel is gonna somehow damage your saw by giving it too much power? or rev too high?