You need to check the technical specifications for this auto. I go on line to one of the Auto Sales web pages (i.e. Parkers), find a model for sale and there should be a page describing the spec of the car in detail, with an additional box called "Tech Specification". This gives lots of info on engines, etc but IMPORTANTLY also includes towing capacity.
A lot of people get this wrong. I saw someone towing with a Honda CRV which has a towing capacity of maybe 1200 kg, which is the weight of an unloaded trailer - not good! It is really important that you work out the weight of the trailer, plus horse ( or horses) plus water and tack, and ensure the vehicle can cope with the weight. Good luck!
Update - just went on Parkers - for an 08 or later Forester the max towing weight (braked) is 2000kg, which is a little light, but possible. Check weight of your trailer. If you only tow one horse, you could probably get away with it.
I tow with a 51 plate turbo Forester (kerb weight of 2000 whatsits). I find it fine as I have an Ifor 401 and a 14.1, although a couple of years ago my ex and I moved a couple of our mares 60 odd miles, the biggest of which was a 15.2 TB and it coped fine.
My sister has always had a Forester - they tow about 2 tonnes so an Ifor and one horse or two small ponies is your max. Tows well and has never had a problem even across some of the rougher fields that are used as 'car parks' for some shows.
My friend had one and used it for towing one horse with an IW 511 trailer. Hers was an 2003 car. She never had a problem although I thought it seemed quite low. I was told that the tow bar needed to be 17" high or something for safe towing.
Yes, we tow a subaru forester with a rice richardson. Fantastic car - tows wonderfully. We only tow one horse in it but have travelled two smaller horses/ponies in it.
Would highly recommend subarus - we have owned 2 and never had issues