There are firms out there that provide similar maps for handheld devices like GPS receivers, iPads, etc. Try searching for "hunting maps" + GIS (or + GPS) and the like on the Web. I don't know of any GIS apps that run on such devices, as such apps require substantial computing power. But "Never say never," right?
QGIS (like many other GIS applications) is used all over the world, even in the Great White North.
You just need to find GIS data layers for your needs and learn how to use them within whatever coordinate system is used in that situation. Note: in this instance, "just" = you'll be spending a
substantial amount of time learning about datums and coordinate systems if you don't know about these already.
Data layers, including shapefiles, raster files and the like are often available from natural resource agencies in each of the states (and from the feds). Sometimes they're out there free for the picking if you know how to crawl the Web for them. Other times (as with the land cover layer used above), you'll need to get them directly from the agency that maintains them. Don't be shy to ask – most of these folks are extremely accommodating on this.
I routinely transfer data layers, waypoints and tracks, etc. back and forth between QGIS and my Garmin GPS receiver, using Garmin's BaseCamp app. There are other intermediary apps out there as well. One that I'm particularly proud to point out is
DNRGPS . (My cousin is Lord of the IT Realm at the Minnesota Department of Natural Resources.)