@witlessbird, passing individual parameters in the URL like you did as fine.  If there are multiple parameters that you are searching on, maybe consider using the scoped_search gem like we do for hosts.  In this case, you assign a string to the :string parameter in the URL like this:
http://0.0.0.0:3000/hosts?search=+environment+%3D+production+and++hostgroup+%3D++Base