Sometimes they do and sometimes they don't. I only have one horse with a splint and right now it is at the initial growing stage so I am not sure how big it will be once it comes through.
To be honest, without some sort of interference, I haven't seen many splints that do become lesser over age.
One of my mares had a BIG splint that went down alot. Nothing happened for about a year, and then it started to go down slowly. Current owner tells me it has now almost disappeared.
A young pony I had on loan developed a splint, I gave her a few weeks off and it got huge but a couple of years later it was much smaller. My current horse came with a splint, it got bigger over the summer but is now half the size it was "originally". So they definately can!
My mare threw a splint aged 4 - to me it looked massive but was probably small to medium sized. I rested her, used cold therapy on it and arnica cream but to be honest it stayed the same size for a long time (6-9 months). Eventually when I had given up all hope of it going, it disappeared! You can just about feel a tiny lump when you run your hand down her leg but it is not visible to the eye.
Had a horse develop a splint high up. Gradually went down over a year. Now a very mild bump. In winter coat is invisible. This splint never caused any probs though.
My boy threw one, I cold hosed it twice a day for 15mins for 2 weekns, then had magnotherapy boot on it for 4 wks, and it has all but gone. Never been commented on for showing, and not visible, you can just feel it.
My horse threw a huge one this summer, wasn't even in work. Didn't do anything with it as he wasn't working anyway just left him in the field. It has recently reduced to about half the size, which i put down to colder weather and rain. He has being back in light work for about about 2 months which has had no effect. I am hoping it will reduce even more throughout the winter.
If it has just come up the best thing is rest. We have been pre training a 3 year old at work (racing) and he's thrown 2 splints on one leg.. he whacked himself in the field. He's now on box rest..has been for a couple of weeks. I work for a top vet and anything that gets a splint is rested, whether it's come up through injury or imbalance in the leg. Magnetic and lazer treatment are good, if you can get your hands on them!
Dmso rubbed in carefully is also good but must be used with caution as can blister...don't think you can get this any more. As the other's have suggested, rest and hosing is as good as anything..and patience. Not all will go down, but work will aggrivate them so let it settle. As long as it's not interfering with tendons I would't worry.
Lex threw a whopper when she was 4 - must have been 18 months ago now. She was lame with it for what seemed like ages (probably about 3 or 4 weeks really) but it hasn't worried her since.
It is still massive though - she is such a tiny horse it seems to take over half her cannon bone!!
Edited to add - she isn't a show horse so I'm not worried what it looks like - have never bothered with any 'potions'.