Several points I want to make so I'm going to line them out and then fill in info on each so I don't forget anything.
1. Tapeworms are not known for causing weight loss and unthriftiness in horses. If you treated for tapeworms then you also treated for all the other common parasites since the only two dewormers on the market that are effective against tapeworms are pyrantel at double the normal dose or praziquantel which is only available in combination with ivermectin or moxidectin. It's more likely that you had a strongyle issues than a tapeworm issue.
What kind of deworming program do you have your horse on? What area of the country are you in? How is your horse kept--pasture, dry lot, stall?
2. Oats are not the best feed for horses. Their balance is adequate though not perfect, but they are not as easily digested. A pelleted feed would be a better choice because they are balanced for horses' and are processed to be more easily digestible.
3. Corn is not high in fat...it's high in carbohydrates which are not good for a horse just like they are not good for humans. In small amounts they can be fine though you need to be very very careful because if they haven not been handled correctly they can contain a fungi that is deadly to horses. And if you want a mix of oats and corn you need to feed a premixed feed because by mixing the two you throw off the balance that you are working for by feeding just oats. With a premixed feed, the producer adds a pelleted vitamin/mineral to provide a balanced diet for your horse.
4. There is no reason to put a 10 year old horse on a complete senior feed and every reason not too if you don't want to be pouring large quantities of feed into your horse daily for weight gain. Complete senior feeds are not calorie dense because they are designed to be fed at rates of around 14-16 lbs per day. A more sensible way to put weight on a horse that can eat hay/grass is to use a pelleted feed that is designed for performance horses because these feeds are more calorie dense and don't have to be fed at as high a rate to provide the same amount of digestible energy. It is cheaper to feed a horse 4-8 lbs of a pelleted performance horse type diet than more than twice that amount of a complete feed daily.
5. Yes, fat provides lots of digestible energy for putting on weight or perfomring, but you should NOT feed used cooking oil. If you are going to add fat to the diet it's very easy to add 1-2 cups of vegetable oil to the diet a day. But you need to start slowly and build up to the 1-2 cups per day otherwise your horse may turn up his nose at his food or develope diarrhea.
Licensed Veterinary Technician