If you can hardcode the fields, then you can do:

require Explorer.DataFrame, as: DF

DF.mutate(df_one_hot,
  animal: cond do
    animal_cat_1_of_2 == 1 -> "dog"
    animal_cat_2_of_2 == 1 -> "cat"
  end,
  color: cond do
    color_cat_1_of_3 == 1 -> "brown"
    color_cat_2_of_3 == 1 -> "black"
    color_cat_3_of_3 == 1 -> "brindle"
  end
)

If you cannot, then you can port your approach to mutate_with. mutate_with gives you access to the columns and allow you to dynamically build a query based on the field. Then use Series.select to build the cond. Scroll down to find the answer (I added some padding in case you want to try it out by yourself before seeing the solution):

categorical_cols =
  df_one_hot.names
  |> Enum.map(&Regex.run(~r/(.+)_cat_(\d+)_of_\d+/, &1))
  |> Enum.reject(&is_nil/1)
  |> Enum.group_by(
    fn [_, group, _] -> group end,
    fn [col, _, num] -> {col, String.to_integer(num)} end
  )
  |> Map.new(fn {group, col_num_pairs} -> {group, col_num_pairs} end)

DF.mutate_with(df_one_hot, fn df ->
  Enum.map(categorical_cols, fn {group, col_to_num} ->
    expr = Enum.reduce(col_to_num, -1, fn {col_name, num}, acc ->
      equal = Explorer.Series.equal(df[col_name], 1)
      Explorer.Series.select(equal, num, acc)
    end)

    {group, expr}
  end)
end)