I'd be happy to discuss various areas in Utah and Western Colorado.

I am assuming you will be traveling thru the area in Early April, So you will have to stay in the lower elevations.  Most of the higher ground will still be snow covered or at minimum wet soggy ground.

If you come up I-15, The area around St George has plenty of high desert terrain to ride.  Several Horse motels or fairgrounds where you can stable horses and of course people accomodation.  Red Mountain to the west of town offers a nice ride with scenic overlooks down into Snow Canyon.  Snow Canyon state park itself has some nice rides inside the canyon.  The Maze over by Leeds is always a favorite ride of mine as you ride thru a maze of boulders and rock outcropings and wonder how the early pioneers ever found their way thru or herded cows thru that area.  And Zions national parks offeres several trails that have spectacular scenery into Kolob Arch and across the Hops Valley.

Bryce Canyon itself is at 8000 foot elevation and may still be under snow. But there are areas around Bryce that are lower elevation and can be road in April. Off of Hiway 12 you can access Casto and Losee Canyons,  Proceed over the mountain and down to Cannondale and into the Grand Staircase Escalante National park an you can ride into Willis canyon.  Also Capital Reef National Park is close by.

If you come up thru the Blanding, Monticello, Moab area, You have lots of desert rides that allow you to see the various indian ruins.  Moab has a wonderful equestrian center where you can board your horses for a night or two. And the area is predominately BLM lands which allows for primative camping almost anywhere you can pull off the road.

Some of my favorite spring rides are along Hiway 24 between Hanksville and GreenRiver Utah.  Goblin Valley is close to Chute and Wild Horse canyons,  A little up the road is Old Woman, Lone Man and Earnie canyons.  All offer narrow canyon rides where you are dwarfed by sheer tall canyon walls. There is a group in GreenRiver ( City council, JC or something) that puts on an annual Green River Trail Ride each April and they will guide the groups thru the area if you are timid about exploring remote areas by yourself. http://www.westslopehorse.com/id15.html.  Across the hiway from Goblin Valley is the trail going into Robbers Roost. A famous hideout for Butch Cassidy and the Wild Bunch.

As you enter into Colorado on I=70. Just about on the State Line is Rabbit Valley and the Trail of Time.  Region IV of NATRC always had an April ride in that area and it offers interesting terrain along the Colorado river to see.

Casto Canyon near Bryce

Willis Canyon in Grand Staircase

Wild Horse Canyon in the San Rafael Swell area

Entering Chute Canyon Near Goblin Valley

Riding in Zions near St George