SASS ignores variables, defined in if-statement

That’s completely expected. Variables have a scope to them. If you define them inside of a control block (like an if statement), then they won’t be available outside. So, what you need to do is initialize it outside like so:

$text-color: null;
$background-color: null;
@if $colorscheme == white {
    $text-color: #333;
    $background-color: #fff;
}
@else {
    $text-color: #ccc;
    $background-color: #333;
}

Or…

$text-color: #ccc;
$background-color: #333;
@if $colorscheme == white {
    $text-color: #333;
    $background-color: #fff;
}

Though it would be less verbose to use the if() function like this:

$text-color: if($colorscheme == white, #333, #ccc);
$background-color: if($colorscheme == white, #fff, #333);