Visa for traveling to Italy

You can use the visa until the very last day of its validity, provided you also fulfill all other conditions (including the number of entries, maximum stay in the Schengen area, having a valid purpose, financial means, etc.)

Do note that in the Schengen area, your visa must also be valid until the last day of your stay. Consequently, if the visa is set to expire in the next few days, you might be asked about your plans.

If your visa is a short-stay Schengen visa, you should be prepared to explain how you plan to leave the country in time (ideally show a return ticket) or somehow switch to another status (apply for a residence permit, get a new citizenship, etc.). If it looks like you actually intend to stay longer without proper documentation, you could be denied entry or even see your visa revoked.

Unlike the visa, your passport (or travel document) must be valid for three months after your intended departure date (so if your passport also expires on February 10 then you cannot go to Italy without getting a new one).

Very much like in this question your visa is valid from 00:00 on its start date, to 23:59 on the date of expiry. So yes you can travel to the Schengen area, as long as you leave before the visa expires.

Having said this, you might have exceeded the maximum number of entries allowed on a single visa. Your visa might in fact be either single-entry, or multiple-entry. It's up to you to check which one applies to your specific case.