You have answered your own question here, I think you just want someone to tell you you should take him so that you can try and dull your common sence screaming in your ear "DON'T DO IT!!" It would be cruel to put an old horse out into cold weather like that. Besides, this trainer is total taking advantage of your good nature. I had basically the exsact same thing happen to me. My trainer OF FIVE YEARS tried to "give" me a aged horse that suposedly had very minor arthritis, (she too had been given him three months before because he was sweet enough for anyone to ride). Anyway, at first I said YES please, then my mum stepped in and said no I don't think so, somethings not right about this. Three months after that he died! Old age supposedly, I was never really told why, (he was only 18!). This is far from the only such story I know. You wouldn't believe how often people are scamed like this. Basically, these people are passing the buck of having to put the animal down.
Sorry I know this is long but, for your question on what is better for him. Definitely light work is a must but freezing cold weather is a BIG NO NO. AND most old horses will do very little movement regardless of the paddock size.
I know its hard, every year I get offered horses "for free".
It will only cause you a whole lot of heart ache to see him in pain, cost you loads of money, and then more money and way more heart ache to put him down and berry him eventually.
Sorry, couldn't you ride your sisters' horses?