<font color="yellow">"That is not a problem, it could be an advantage. "</font><br /><br />Hydrogen boils at 20K, oxygen freezes at 54K. This makes it a problem.<br /><br /><font color="yellow">" The warmer the Hydrogen, and the higher the pressure, the better"</font><br /><br />Hydrogen is usually stored already at the boiling point. There's continuous boiling going on inside the tank but the insulation keeps it at manageable levels. IIRC just before liftoff the tank pressure is raised to 'flight level', which helps temporarily to minimize the boiling.<br /><br />From hydrogen's point of view even frozen oxygen can be 'hot' and LOX is <i>burning</i> hot. Uncontrolled exposure to LOX temperatures may cause violent, almost explosive boiling. Hydrogen's density is low enough even as pure liquid so we really don't want to pump anything but liquids. And cavitation would break a turbopump anyway.<br /><br /><font color="yellow">"The colder and denser the Oxygen the better"</font><br /><br />Sure but you'd have to be extra careful not to freeze the LOX. Unshielded LOX line through liquid hydrogen tank would freeze solid in no time. And before that chunks of frozen oxygen might come loose, get sucked up to the pump breaking it and/or clogging up the injector holes.