In the general terminology and specification of the binoculars the compact hunting binoculars are those which have less than the aperture less than 30mm.
The compact binoculars for hunting based on the specification that we have specified above will not be able to have a good hunting as the size 30mm is not very good. Generally the best binoculars for hunting will require the hunting binoculars to be have the specification as 7×35 or even 8×42.
Some of the best binoculars Leica Ultravid Compact 8×20 and the Leica Ultravid Compact 10×25 in the compact category.
Another which is the e Zeiss Victory B T* Compact 8×20 binoculars and Zeiss Victory Compact 10×25 binoculars are very good compact binoculars. These are very highly costly though and these definitely do not fall under the budget category.
Bushnell Legend series are also very good in the compact category and that will mean that you can have
Steiner has compact binoculars which are Steiner 12×40 Predator Pro Compact Hunting Binoculars
Roof prism binoculars are generally compact in design than the porro prism binoculars. For more detailed design considerations you can read about these in my post here on roof prism versus porro prism.
In general the advice is that as far as compact binoculars goes that do not use these binoculars if you are really serious about hunting. Use them as a second pair .If you a kid going along with you on a hunt then these are the best as the diameter of the objective lens is small.
These are easily pocketable.
As far as the usabilioty goes because of their exit pupil being less they will not very great.