Florence in February

I've spent approximately 30 Februaries in Florence during my lifetime.
I don't think there are hotels that close in February, if there are they would be very few marginal small ones.
I don't know what tourist activities you refer to, but all museums are open, except for any possible scheduled weekly closure (for example the Uffizi close every Monday). Restaurants will also be largely all open, and so most gelaterie, which are obviously more popular in summer.
Students can be anywhere. There are literally dozens of International schools and universities in Florence, including many international satellite campuses of famous American universities (e.g. Stanford, Syracuse, Pepperdine, Harvard), and they are located at several sites, so you need to inquire with your grandson where he's enrolled, however many are in or very near the historical center, so they are closed to all sights.
Wine tours should be available all year round, many wineries in the Chianti area offer tasting in winter certainly on weekends.

I was one of those students. Roberto is correct; Florence is a vibrant and fully functioning city every month of the year! He is so lucky to have lived there; I wish I could have lived there longer than my year of study.

February is a great month for fewer crowds. One thing to look up is the dates of Carnevale in Italy (Venice, Viareggio for example) and France (Nice, for example), That might be an amazing experience for both you and your grandson.

It makes sense to visit in February as the city as not as crowded as in full season. The possible cons are that the weather is colder than in spring and daylight time is shorter. But the city is in full activity - on the contrary, Florentines will leave Florence in August and maybe also in July for the unrelenting heat. The tourist machine goes on working, but in August many shops may be closed for holiday.

I was in Florence the first week of February this year. I found no shortage of tourists or tourist activities then (though I did not do any tours). I saw many, many students out and about in the city. I visited several museums, walked for miles and ate gelato every day. The weather was chilly and windy, but sun every day while I was there. It was crowded enough in February that I thought 'what must it be like here all summer'??

In February, you can take one or more of the British Institute of Florence's terrific art history classes and site visits: https://www.britishinstitute.it/en/history-of-art/renaissance. February is when they cover the Renaissance.

Thank You all so much. This helps so much. And I will schedule the wine tour on the weekends and the British Institute looks fabulous. Thank You, Thank You, Thank You.