I do not believe that there is a rule in the game that prevents me, when I am shuffling, looking (and even counting) the sorts of cards that I have. Would it be possible to add a feature where I can see what all I currently have in my deck? I am thinking that when I hover over my name (where I would normally see the cards I have in exile, set aside, etc.), I would see a current deck inventory. This would be helpful in many, many instances. Granted, I should not have access to that information for other players.
That is against the rules. You shuffle cards face down, so can't look at them while shuffling. You cannot count cards while shuffling, but you (and your opponent) are allowed to count the cards in your deck, that's why everybodie's deck contains a number, indicating how many cards are in it.