We have trained our poodle cross to like having his hair cut. He came from a refuge and hated it at first.
How? We started gently, giving him a tiny reward before cutting anything, and then every ten seconds, repeating, "Good boy!" if he didn't growl. It took several sessions and we didn't try to cut everything in one go at first. Now he accepts hair cutting without protest, as he knows he will gets a treat at the end if he behaves well.
The hair is easier to cut when it has just been washed and dried. It also makes cutting round the bottom a more pleasant experience, LOL!
Regarding muzzles, I would say that it is generally possible to train a dog to be cut without one, and also do not use one in very hot weather, as it restricts their ability to pant and can cause fainting and/or heatstroke.
If you really cannot manage without a muzzle, the easiest way would be to buy a cheap fabric type muzzle and cut away round the eye area if you need to clean the brownish-black stuff which comes out of most poodles' eyes. Or you could have a look at this page: http://leerburg.com/muzzleselection.htm and click on the "wire basket muzzles" link.
Our dog has been trained to accept having his eyes cleaned, as well. We usually clean them during our dog's shower, where the wet helps to make the deposits more pliable for removal.
Every best wish to you! Please go to the introductions section to tell us all about yourself and your pets, and feel free to post a picture as well!
(BTW the dog in my avatar is not a poodle cross. She is a dog we had previously).