thanks for your question. In fact, there was a full moon on February 10, 1865, according to the U.S. Naval Observatory, which provides dates and times for the lunar phases between the years 1700-2035.
Since the Moon takes about 29½ days to go through an entire cycle of phases, every once in a while we'll just miss having a full moon in February--most recently in February 1999.
Because the Moon reaches its full phase at a particular instant in time, whether or not you have a full moon in February can depend on your time zone.
For example, in 1980 the Moon was full on February 1 at 2:21 Universal Time, which is five hours ahead of Eastern Standard Time. For someone in England, that full moon occurred in February (just barely). But at the same moment in North Carolina, it was still January 31. Since the next full moon wasn't until March 1, we had no full moon in February that year.
The next February we'll have no full moon will be in 2018.