Florence weather in Oct - should we still ask for AC?

I don’t think it's needed in mid October. Generally it will be around 75 max during the day. Some years it might get warmer during the day to around 80-82F, although not too often, but at night it will drop to the low 60s if not lower. If it is warm during the day just open the windows in the early evenings and the rooms will cool down quickly. Carry an umbrella in October.

Let's put aside ethics, I am not even sure you CAN turn the AC on in October.

Some years ago we were told by our hotel that the government prohibits AC after a certain date, and it was sometime in October. Did I understand correctly? This was in Padua. We had AC when we stayed there a few weeks earlier in September; when we later returned for one night I went to the desk to say our AC wasn’t working. “È finito per noi” ( It is finished for us) as my poor memory and weak Italian recall. That was the explanation. Good luck and safe travels.

If memory serves there are restrictions on when you can use heat and A/C. But mid-October should be fine, especially in northern provinces. This site is useful: https://www.timeanddate.com/weather/italy/milan/historic?month=10&year=2021

In the City of Florence heating can be turned on from Nov. 1 to Apr. 15 for a max of 12 hours daily. There are several zones (A, B, ..) and each zone has its limits. The City of Fiesole, next to Florence, being higher in altitude, belongs to a different zone and they can turn on heating for longer.

I don’t think they have enacted time limit rules on A/C yet. The only limit enacted last Spring after the Russian invasion, was to have A/C thermostat temperatures at no less than 25C (77F) in public buildings (with exceptions, for example hospitals, etc.).

I'm reluctant to say that we did often use the AC in the last week of September and the first 10 days of October in 2018.

Padua's temperature was fairly comfortable and we had a door wall that opened to a private balcony. It was screened and allow cool air flow. We did find plenty of mosquitos during our evening visits to Scrovegni Chapel. Our unscented insect repellent came in particularly handy while we waited outdoors in the evening for the extended evening reservations.

We used the AC in Venice when our room was being invaded by mosquitos and the window had no screen. It was also warm enough several times to justify use.

We also used the AC in Florence as our window was again not screened. They gave us the plug-in mosquito device but it simply wasn't working. It was fairly warm and humid enough so it seemed reasonable.

In Rome our window couldn't be opened so AC was really needed. It was actually very warm and sunny for our week there. I'm glad I found Avene sunscreen to use during our time at Ostia Antica.

Hopefully our AC consumption wasn't unethical but the AC was available and thankfully working for the high mosquito population and heat.

As someone who keeps the temp at 73F at night, should I bring a sweater to sleep just in case for my trip to Florence at the beginning of Oct?

I've wondered the same thing. Quite happy to be a bit too warm, but worried about being cold during our travels in mid- October.

We were in Padua the last week of September where we needed jackets outdoors several days and evenings. It became warmer during the next 2 weeks as we traveled to Venice and then farther south the next 2 weeks of October. I don't recall ever needing a sweater or jacket. We only had a light rain one afternoon in Florence and one day of periodic rain in Rome. It was mostly warm and sunny from Venice to Rome. YMMV as clearly weather varies greatly year to year. We were fortunate to have mostly warm sunny days.

Usually AC is not needed in October in Florence.

In any case, consider that Europe - Germany at the head - is a in a big energy crisis as it relied on importing Russian gas for electricity production. Russia was sanctioned and Russians are retorting by strongly limiting gas exportations. The price of electric power has skyrocketed (say, two/three times what it was one year ago), factories and restaurants are already complaining they cannot stay in business, and I am expecting that after the September election some serious energy economy measures will be announced. So, even if you find an apartment with AC, I would not expect they will it switch on. Too expensive in the best case, forbidden by government if the worst comes to the worst.