My dad just installed 3 flood lights on my trailer for outdoor lighting and suggested I use a solar panel for keeping the battery charged.  Any suggestions on the size of panel I'd need to keep the 12v battery charged?

Welcome to the forum..

Your question needs more details for a complete answer.  All batteries lose some of their charge just setting.  If you merely want to (maintain) keep a charge then Deranger's suggestion is right.   

If you want to recharge the electricity used by the flood lights, you'll need a significantly larger and more expensive solar cell array.  You could figure the size by added the watt draw of your 3 lights and buying an array of that wattage.  The you'll have a situation of being able to use your lights about the same time the solar cells are charging.   5 hours of full sunlight = 5 hours of flood lights.  Or NOT, double the charging time, means halving the cell wattage,  Or doubling the cell size means halving the charging time.  You'll have to chose money for a solar array or light time.

he ones you see on the dash of cars are usually 2-5 watts. Not enough to worry about running flood lights.

I don't know what wattage your flood lights are.  But for example look at using three 100 watt floodlights.  To run them for 1 hour would take 300 watts.  To recharge that would take you 60 hours of good sunlight with those small solar cells.

Most of the RV battery chargers you see are 20 watt units and cost around $300.  Headlights on most cars are 50 watts for low beam and 55 or 65 watts for high beam. So if your flood lights are as powerfull as a car's headlight, you will consume  50 watts x 3 = 150watts per hour. If you get 10 hours of good sunlight in the summer (no clouds or overcast) you can expect to generate 200 watts. (20watts x 10 hours ) Which would power your lights for an hour and 20 minutes. Which may be fine for the 10 minutes it takes to saddle or unsaddle a horse. But may not be enough to cook dinner and read a magazine.

In addition to a charger, you need a battery with the capacity to store the power you generate.

In general terms, if you just want  a few minutes of light for loading-unlodading, saddling etc the charges may be fine. If you are camping and want to light up a camp site, you are better off with a Propane lantern or a generator.

Thanks for all the help.  I think the lights are 50w a piece, set up with 2 lights on one switch and one on the other, and I won't be running them all on a daily basis (mostly the 2 on the tack room side every other day for 20 min or so), but I do want to have enough juice to be able to run them for a bit longer if I had trouble on the road or setting up camp or something.  Would it be feasable to install a 10w with a charge controller, see how it does and then add another 10w later? I plan to put them on the front of the trailer on either side, (I have a fiberglass roof, steel trailer) and live in a sunny location.

Jill