The new store exclusive steed of June is the Steed of Rhûn. This steed appeared in the store starting on June 1st and will be available until June 30th.
Here is the full size screenshot Turbine has on their web site.
The description of the horse in the store is:
This steed has barding made of sturdy leather banding and light cloth.
This mount is as fast (+68%) and same morale (250 HP) as the previous store exclusive mounts with the same price tag. This steed is a per character purchase so be sure you spend the Turbine Points on the character you want riding this.
Purchasing this steed will also allow you the use of the appearance items for your War-steed.
Store Location: Travel & Housing -> Mounts -> Store Exclusive
I took a couple pictures of the war-steed model that is sitting in the stables in Snowbourn to compare what it looks like in game.
If you have purchased this mount and would like to share screenshots, please send us. We are particularly interested in which areas of the war-steed cosmetics dye.