Horava gravity is a horrible attempt to solve the divergences of quantum gravity.
Basically it tries to introduce a cutoff. This is done at the price of breaking the symmetry between space and time.
The associated mathematical framework is ugly and contrasts with the beautiful framework of Einstein's gravity.
As a matter of fact, the divergences of quantum gravity can easily be removed using much more elegant frameworks. These do respect the symmetry between space and time, and try to remove divergences either using covariant cutoff, or by other mathematical techniques.
If you are interested in relevant theoretical papers, you can search for divergence-free quantum field theory and divergence-free quantum gravity.