This is very common. It's a very rare dog that makes any connection between what's happening outside and the need for a coat or harness.

As far as they are concerned you are subjecting them to a straitjacket for no reason. We can't explain to dogs so we have to train them. This has already been mentioned in an excellent answer by @Elmy.

From personal experience I know that it's possible to train a dog to *approach* a collar, coat or harness and put their head through it. This is all done with treats. An extreme example is the dogs that have been trained to place themselves and [lie quietly for a brain scan in an MRI machine](https://www.youtube.com/watch?v=Q5sXqk4j9jk) 

Training is a skill that needs understanding and patience on the part of the trainer but the rewards are enormous, (1) you are happier (2) the dog is happier (3) you get compliments from everyone about how clever and well-behaved your dog is.


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> As soon as she sees the harness she will run and hide under the
> furniture. Sometimes its a bit of an ordeal to extract her.

This is the biggest part of the problem. The whole procedure has turned into an unpleasant experience. Instead of the harness being a signal that you are about to go out, it is now a signal for being chased and wrestled into submission.

Trying to find a hidey-hole and then being pulled out of it is scary for any animal. They like to believe there is somewhere that they can get away from any risks or danger. I never try to force a dog to come out of its kennel/bed/crate against its will.

The answer for that is to allow them a safe place that really is safe - maybe a particular spot under the furniture or behind the settee and keep that sacrosanct, only cleaning or tidying there when they are elsewhere. 

My new small dog has recently taken a dislike to her coat - The Velcro got caught in her fur once, it must have been uncomfortable to walk and I only discovered the problem when it was time to take it off. It only takes once experience like this for them to remember and get worried.

I haven't got round to training her to approach the coat yet (this is a timely reminder!) and so for now I just put her on the lead as for any walk and then pick up the coat afterwards and slip it over her head by passing it along the lead. This way she has no opportunity to run and hide and so we avoid any drama.  In fact she's quite happy for me to do this now.

A collar and lead to hold them still until they are trained allows you to bypass all the  drama as well as the gymnastics and wrestling that go along with it.