Gutters are always a great idea.
I had the same issue. I put $3 masonry disc on my grinder and made small drain grooves away from the door outward to get by until I had more time. I used a piece of metal to lay in the track that I cut to put a level on top of it. I did that so I knew I had a slope on it as its hard to tell.
Eventually, I went and got a wheel for my 7" grinder, $5 at local hardware store. Marked a reference line with the door shut, so I knew where it lined up. Then I open the door and ground a slope on the entire thing. Occasionally checking it with a level for humps and angle, was easier than I expected. It looks really good, nice and smooth, other than some polished aggregate in the surface now you cant even tell. I did put some sealer on it, just in case.
If I had to do it again though, I would wear a better mask. You have to do it with the door open for room to work, so consider taping up the doorway with plastic because the dust will go everywhere. And on the ends when you get close to the wood sides. Put a piece of metal or something against it so you can get close in and neat, without damaging the garage. Or just be careful. It was a nice permanent fix for mine, and even when snow is up against the door melting, it doesn't come inside anymore. Hope that helps.
