First off, you have to be able to read sheet music fluently. If all you can do is improv and playing stuff from memory this article will be of no use to you. Sorry :(.
Now that we have that off our backs, lets begin.
Okay, so first you have to determine a few things like if its for a marching snare (I may write another article on basses and tenors) or concert snare. Marching snare will be much more rudimental, so get acquainted with them. Concert snare is pretty much whatever feels like it should be.
The way I write marching snare drum SOLOS is I pick a few rudiments (they can be your favorite or just some random ones), and I come up with a couple cool rhythms/beats. Create a rough draft score sheet, and write down anything you think can fit somewhere. Go ahead and write it in the music or just write it out on a separate sheet of paper and put a little note saying which measures you think it will sound good between. Then simply refine it an and more then repeat that until your song is the desired length.
With marching snare drum music where you play with the rest of the band or corp is basically the same as solos, but dumb it down a bit (so it doesn't over power the piece), and make it fit the music in its own distinct way.
The way I write concert snare drum music is basically whatever the heck sounds good. Develop some thoughts, write them out, and try not to refine it A LOT. A little bit of refining is okay, but try not to over work the part if you know what I mean.
I could go into further detail, but your music will start to be moulded by my styles, so try and develop your own! Thanks!