In this context, "eyes severe" likely refers to Hotspur's intense and sharp gaze, perhaps hinting at his quick temper and readiness for battle. "Beard of formal cut" could refer to Hotspur's carefully groomed and stylish beard, which might give him an appearance of seriousness and formality.
Together, these traits suggest that Hotspur is a disciplined and serious warrior who is not afraid to confront his enemies. His fierce gaze and well-groomed beard could be seen as symbols of his strength, determination, and adherence to tradition.