Horse1sense, I live in No Utah also, but have made many trips down. I have ridden Wilis Canyon, The areas in and around Bryce Canyon, Thunder MT and Red Conyon.
You may want to check with Camanae over on GaitsofGold website under the Misc Gaited Horse Discussion. He is the moderator for that discussion. He lives in Kanab and ranches the area between Kanab and Bryce. He is also a member of the Kanab Back Country Horsemen.
Another area you might consider in April/May is the San Rafael Swell area. I spend more time over there than I do down near Kanab. It's an hour or two shorter drive. It has fewer people, more remote. You can ride the canyons to the west of Hiway 24. We have camped at Buckskin Springs and made a loop up Chute Canyon across the back of the swell and down Wild Horse. Or do the same a little farther north. Camp at Lost Springs and ride up Lone Man wash across the back and come down Ernie Canyon. We have also pulled off I-70 at Justinson Flats and ridden the horses down to Copper Globe mine and out to the Window over looking Red Canyon. Alos read the article I wrote about San Rafael Swell's McCarty Canyon. I posted it in the article section of this website. http://www.horseforum.com/horse-articles/san-rafael-ride-42378/
Check the website for both the Kanab and Price Chapters of Back Country Horsemen. They have monthly rides scheduled that you could join. Once you get to know the folks, they will share many other trails that you could ride..