This is all normal. When the bow is on the string, you can give into the force of gravity. You can't when the bow is in the air or else you will drop it, so it makes sense that you would tense up because you're trying to keep the bow from falling. Some beginners don't trust that the violin will support the bow and feel like they are losing their grip while playing. That's the kind of tension that will get in the way of your technique and not what I believe you are describing.
That being said, excess tension in the body isn't good, in terms of injury prevention. It's really just not a good idea to hold your bow horizontally in mid air. Use your left hand in the middle of the stick to support it or rotate the wrist so that your bow is vertical, instead. If you are trying to work on right hand technique only, hold a pencil or bow on an open string, so that you don't strain your hand by using the bow without the violin to support it.