I wrote an answer to this but it didn't appear, someone said to enter by hot threads so trying that.
Although I am a keen gardener I am also a rider and I feel it is a shame to get rid of an arena which a horsey person would give an arm and a leg for. They can add value to a house and, if made properly, can be very expensive to install. If it is just bark on soil it may be possible, but it will be acid and lacking in nutrients as fidgetbones has said.
If made properly there will be foundations and possibly a membrane. Have you dug under the bark? If that is the case, it will be difficult to make it into a garden without some heavy machinery.
By the way it is a Manege not Menage. It is a French word and menage in French means "housework". A "manege" in French is a covered arena. Programmes like "Escape to the Country" get it wrong all the time. Strictly speaking it is not either as it's not covered, it is an arena or a school (for horses!). Sand ones are "sand schools".