I don't have that much of a slope, but when it's icy it can be significant, and even a tug has a tough time. A few years back, in the winter, I relied on a 12v Harbor Freight remote control winch. It was cheap at about $60, but really kind of sucked overall.
Just recently, to help the girls out all year, and for me in the winter when it's icy, I just got done putting together a new system.
I bought the same Harbor Freight hoist that others are talking about. It's $129.99 and I got it at 25% off of that on the last big sale. So under $100.
It does have a handheld cord that you could extend. It runs on 110V and is actually made very well. It feeds about 32 feet per minute. It has a hard stop that will shut it down if it gets pulled all the way in. You could attach a lead on to the hook so that the winch will stop for sure before the plane hits the winch. (I'm calling it a winch but at Harbor Freight it's technically a "Hoist")
What I did to mine is a bit different. I bought a Linksprite R4. (Think Arduino, with built in wifi and 4 relays). I set it up to be run via a web page (internal only) from my iphone, with various runtimes. So I can hit a button and extend the cable 45 seconds, for instance. Then I can hook it up, and hit another button to retract for various times, from .5 seconds to 30 seconds. I can also hit STOP at any point and shut it off. But this way I can feed it 10 seconds of retract if I want, or 5, or 2, or whatever, so it goes slow if needed. It all runs on the wifi at the hangar.
I'm guessing that some of the winch remotes could be modified similarly, or you could simply extend the control cord.
Anyway, it's not a "perfect" option since it doesn't come with a wireless remote, but you can certainly improvise with it and from a mechanical standpoint it's cheap and solid. I'd love to have a tractor but in a T-hangar it's just one more thing to get in the way and to maintain, for me.
The tugs are definitely expensive. I have 2 types of tugs, and neither is ideal.
The one from WagAero can do a reasonable job pushing planes around and can be connected remotely. The other is I think a minimax, and that one is more of a pain to manually hook up but is much smaller and lighter. Neither one does a good job of turning, so they both aren't fantastic. That's why I went the winch route for the girls. I want to guarantee that the wife and daughter can get the plane back in the hangar anytime they need to, and that will do the trick for sure.