I agree with interpreting the "seint" part as referring
to the king's reluctance or lack of enthusiasm for Auðun's
departure, not necessarily involving anger.
As for "um hríð" I don't have any straight answer.
How long is "a while" anyhow? I'd guess the range of
meanings is quite similar. At least I wouldn't hesitate
to translate one with the other.
I don't think the phrase "nakkvarar stundir" made it
into Modern Icelandic as such. If you were to use it
now it would probably be interpreted literally as
"several hours".
The phrase "um hríð", on the other hand, is alive enough
and would not be taken to mean "for the duration of a
snow-storm". :)