I used to live in that area. The answer is no, "the great sandhills" themselves are provincial park or land (I forget) and all of the others are owned by ranchers. Now if you are good friends with those ranchers then you are usually free to ride them (like me ), but other than that it is a no.
And to be honest they aren't all that great, about 90% is grassland, 10% is actual sand dunes, and the tallest don't rise over 80 feet at the most. Nothing to make a trip from edmonton for.