In Bohnanza say I have 5 cards during a round.
Another player is in his trading phase and I trade a card with him, I put the traded card on my trading area and then plant it on my field.
I'm now down to 4 cards so, do I have to take a card from the pile for the one I traded?
To the best of my knowledge, there is no "minimum hand size" rule in Bohnanza.
The active player draws three cards at the end of his round, but it's perfectly possible to start your round with no cards at all in hand! As demonstrated by this line in the "1. Plant bean cards" section of the rulebook:
So, no, you don't draw to replace cards you used in trades, at least not in any variant of Bohnanza I'm familiar with.
The other answers are right, only the active player draws cards. So the standard-rules make it possible that you empty your hand through trades.
The extension Ladybohn offers a rule variation. Instead of the active player drawing three cards, everyone draws one card at the end of the turn. That makes the game faster for higher numbers of players. We usually use that rule, even if we don't use Ladybohn.
No. There is no where in the rules to indicate that this would be the case in any situation. The rules clearly state that
Beyond this, there are no other actions the non-active players make to process a trade. The rule book mentions in a side note
The point of trading is to get cards out of your hand, so replacing them with new cards by drawing would be counter-productive.