Can you hide your cards so other players can't see how many cards you have left? So if you don't remember to say UNO, others can't know if you had only one card left.
The official rules of most games tell you what is allowed, and usually only tell you what isn't allowed when it seems that it would be possible otherwise.
For instance, there is no rule that says I can't add four cards to your hand whenever I feel like it. (feel free to add your own ridiculous rule here)
Should this be allowed because the rules don't specifically prohibit it? No! Of course not! The rules can't possibly list everything that's not allowed.
It's an important part of Uno that you can easily tell how many cards your opponents have so that they can be penalised for not calling "Uno" on their last card. The only way they can get out of this penalty is if the other players don't say anything about this before they can play their last card.
So, no, while it isn't specifically prohibited, it's not legal to hide your cards to gain an unfair advantage.
Of course, if you have a house rule that says you can do this (and all the players have agreed before the game began), it is allowed. However, you're not truly playing Uno anymore, just a game that's very similar to Uno.
This is not banned by the rules - and does not remove information from the game
From the official rules: https://service.mattel.com/instruction_sheets/42001pr.pdf
There is no rule stating how a player must hold their hand. The only relevant section, is that you must declare UNO when you are down to 1 card, and that if you are caught - you must draw 4 cards.
As such, it is "legal" to hide the cards.
That said, most people play UNO with friends for fun. In such a setting, you would absolutely be breaking social norms - and I would be surprised if many people want to continue playing with you, as such behaviour would be considered against the spirit of the game by many.
However, the reason it does not matter from a game perspective - is hiding your cards does not change the game mechanics at all.
In UNO, players have enough knowledge at all times, to calculate the number of cards any other player is holding. There are no hidden cards, or cards that are not played to the center of the table, and likewise, all players start with 7 cards - as such, by following the cards that have been played, it is always possible to track the (number of) cards somebody must be holding.
As such, the game does not change at all by hiding your hand on a fundamental level - but as with any attempt to rules-lawyer in a game designed to be casual fun; you will very quickly gain ill-sentiment and people will simply stop playing with you.
You can but it is, at best, pointless. People are just going to end up calling Uno on you all the time, only for you to show that you have more than 1 card left. There is a chance that people will get complacent if you do this all the time and forget to call Uno on you. There is a much greater chance that you will annoy people and they won't want to play with you anymore.