Feeling bad, please don't beat yourself up about this.
I think there's two things here: firstly the row itself, and secondly general bad vibes and your unhappiness.
Taking the row first - well, you should hear the ding dongs we have in our house. Our 7 year old even enjoys joining in now and passes comment as we go. My husband is a loud man with a short fuse at times. I am none of these things, though I have learned to give as good as I get. I had to. Rows are how we sort things out,let of steam and prioritise things - sometimes! I avoid them if possible though, for more peaceful means of communication.
We try to have rows when the children are in bed and very,very, rarely resort to personal insult. They are usually about minor houshold things. I know underneath, my husband is a loving and good man. But being loud (sometimes), and temperamental is part of his personality. I can't hide that from the children. If they see him throwing a wobbly, (I usually go quiet and get stern) we make a big point of being very loving to them aferwards. I've told my oldest son that his father's bark is worse than his bite. He's got that sussed. I really don't feel guilty about my children witnessing the odd row kept within these limits: Quick, non-personal and a public making up soon after. It has done them no lasting harm that I can see. So, in your shoes, I wouldn't worry too much about the odd outburst like this.
As for the general bad atmospere - this IMO is where the problem lies. If your husband regularly insults you in front of the children, doesn't publically make up with you after rows and lets a bad atmosphere linger for days, IMO, it could well affect them for the worse. In the long term, it may make it harder for you to get your children's respect when you discipline them. At the moment, it's going to confuse them as they try and work out the rules of good and bad. I suppose you may well have bought this up with your husband. If you'd had any joy about this, I guess you wouldn't be posting here.
You sound so fed up after this outburst. If you are generally unhappy, then that's what your children could sense. It's difficult IME to give your children your full attention when your mind is elswhere. When I've had problems of one sort or another - as we all do - my children's behaviour has changed for the worse. I didn't notice this when they were babies, but as they got to three and four, they were aware of mummy's wandering attention and short temper on 'off' days.
However, isn't that part of growing up in any family? No one can have a perfect disposition all the time. And when I became nice mummy again, the behaviour IMO seemed to improve, with no huge long term effect. You say your three year old has been acting out of character recently - well yes, it could be that they are picking up the bad vibes, though equally there could be a thousand other non-related reasons.
I am rambling a bit, so I'll stop. I suppose I'm saying life isn't an American sit com. Don't take on all this guilt about the rows. As for the long term bad atmosphere, that's needs to be sorted out somehow with your husband. Hope this makes sense.