Would there be a substantial enough of a horsepower boost to be noticeable?
The most you could see from such a modification is 15hp. This would not be enough for the seat dyno to register, unless there are plenty of hemorrhoids to detect it. More then likely you'd see a measly 5-10hp, and then only at the higher RPM levels would this be apparent. You would only be able to see the increase via a chassis dyno.
Would the truck perform in the rain as well as before?
Depending on the modifications made (I'm unsure of the CAI you are planning to use) your truck won't have any issues using the CAI, nor will it have any issues in the rain. Even CAI's that utilize an exterior intake (as you've suggested in your question) usually have a drain the bottom which allows for any water which may enter to leave as well. You'd have to drown the entire truck to have an issue.
Is it safe to put this kind of performance part on an old engine with high mileage?
It won't hurt anything ... but really, it won't help anything either. The engine will only use the air it can take in ... no more, no less. Allowing it to breath a little better won't hurt anything.
If you are getting these modifications for free, then no big deal ... put them on. If, on the other hand it might cost you money, I'd suggest you pass. It's not a good return on investment for your truck.