spring the weather can still be at its worst down there. often doesnt settle down till early to mid january, autumn can get a lot of settled weather but can get the odd pre winter storm but its generally more settled than spring....
it varies from year to year but spring usually isnt good, you can get snow storms at xmas... I go down most summers and more often than not theres a off crap weather up till new years and even after. thing is there are quotas on teh no's of people who can do those walks so it doesnt matter so much, the huts dont get over crowded once you have your booking.... the milford will be fully booked right through till autumn. not so the kepler...
fit the routeburn in if you can , i like it better than both of those walks... it's two to three days, its one way to get back to queenstown...
this spring the weather has been pretty bad in that neck of the woods. we've had a lot of storms go through, last summer wasnt the greatest either.
but autumn was brilliant and of course i was injured. cascade saddle is another great one, weather allowing... usually done as a fie day trp as part of the rees dart, or three and a half days as a through trip from wanaka through to glenorchy..
from what i can tell southern nz's weather is similar to tasmanias....
http://www.topomap.co.nz/
from the land of the long white clouds...