I hope I'm not overstepping my bounds, but as a Latin student I'm always eager for a chance to put all that studying to use
Working from the English version, the first portion of the prayer I would render in Latin as "pudicam benignamque deam deumque magnum cornutumque, nunc laudo." I omitted the description of the Horned God as "proud and strong" because there is no positive word for "proud" whose meaning is not already covered by "magnum", and in order to balance the epithets - two each for the God and Goddess. The description of the Goddess as "pudicam" gives the sense of "pure and chaste"; I wasn't sure what sort of "pure" you were going for, so I assumed it was a reference to maidenhood.
The second portion contained more idiomatic English phrasing, and, as I was uncertain of my ability to accurately translate it, I made some dramatic changes. My version reads "Expurgate me cum redeat ver.", translating as "cleanse me while spring returns" or "cleanse me when spring returns."
The full text of the prayer in Latin is then "Pudicam benignamque deam deumque magnum cornutumque, nunc laudo. Expurgate me cum redeat ver.
Please feel free to correct my Latin; though I have been studying for a few years, I am still only learning! Allthepacas, your Ostara prayer is beautiful; thank you for sharing, and I hope you do not mind me having a little fun with your grammar! I love Latin too, and it's always wonderful to see what is being written in a language that is, in many ways, still very much alive.