> And defining a function that will only accept particular variant is nice

This is possible to achieve (or hack your way through, if you will) by parameterizing the type and using a nullary type (a type which is impossible to have) to exclude specific cases of a sum type. In Haskell this would look like this:

    data Weather a b c = Sunny a | Rainy b | Snowy c

    -- can't snow in the summer!
    onlySummerWeather :: forall a b. Weather a b Void -> String
    onlySummerWeather weather = case weather of
      Sunny _ -> "Got sunny weather"
      Rainy _ -> "Got rainy weather"
      Snowy v -> absurd v

where `absurd :: forall a. Void -> a` "if you give me something you can't ever have, I will give you anything in return".