The children always* inherit the father's hair colour. So if you want a red haired Severa, you'll need to pick red hair for yourself.
*Except female Morgan inherits the mothers (the person your male Avatar marries). Lucina is always blue. --- "When playing a game, the goal is to win, but it is the goal that is important, not the winning." -Reiner Knizia
The only reddish hair colors Severa can get (when not using the Avatar as her father) comes from Gregor (auburn, on the organish side) Ricken (auburn, on the brown side) and Gaius (orange).
Otherwise, she can get the hair colors of the other potential fathers, from Frederick's brown to Henry's silver/white. --- "I bought a ward against [logic] off a traveling fortune-teller. It lets me add two 'n' two and get a pickle."
Oh ok. So what are the possible hair colors for her while I'm trying to marry her?
Assuming you've already started the game, whatever you picked at the start. You're stuck with it, sorry.
If you're still planning the file, check the colours in the avatar creation. There's like 20 colours, I think most are roughly equal to other characters already there. --- "When playing a game, the goal is to win, but it is the goal that is important, not the winning." -Reiner Knizia