But since this is the Social Security & Medicare group and the OP seemed worried about Trump possibly cutting Soc Sec benefits that's what I was trying to explain so people who are elderly and/or disabled, as I am, wouldn't be stressing needlessly.
Anyway, as I stated above, For Soc Security COLA there's just the one formula. (<The link goes to the Soc Sec Admin site.) There's a link to the 1973 Soc Security Act that details the formula/how increases are calculated on the page too.
Anyway, Obama alone couldn't freeze (nor would he have) COLA for recipients of Social Security. It simply wasn't in his power to do so as I addressed with links above.
OTOH he could and did freeze raises for fed employees since that's something that can be done by a president.
The reason Soc Sec recipients didn't get increases for a few years wasn't because Obama froze us. It was only because inflation was low and our cost for Medicare Part B went up enough to cancel out what little we might have gotten. The way our benefits are calculated and the increases for Medicare have made it so our buying power has diminished. Obviously how our COLA is calculated needs to change. IMO this an issue Dems must address and push to fix and NOT with the 'chained cpi' bull.
I tried to find info on fed retirees COLA being frozen but I'm not seeing that as having happened either. It's possible I'm missing something since I'm extremely tired and rushing a bit ATM but all I could find is discussed in the WaPo link a couple paragraphs up.
I'm not saying that the Republicans couldn't band together and TRY to change the Social Security Act in a way that would harm seniors and disabled beneficiaries. I tend to think it's extremely unlikely that they'd get enough willing to commit political suicide ATM though.