There is no role of prophylactic seizure treatment in neonates. Maximal caution is warranted before prescribing potentially neurotoxic drugs (such as phenobarbitone), particularly to infants without seizures (by definition HIE Sarnat gr 1). Treatment should be limited to neonates with a significant seizure burden verified by aEEG/EEG. Also it is unclear to me in what way PB would "help" in CV stabilization.
I totally agree with johan. there is no need of prophylactic phenobarbitone therapy becoz most of the cases of HIE stage 1 recovers with supportive treatment and they never developed Seizures.