My horse used to refuse to be caught to, where sometimes it escalated to jumping the fence into other pastures. I fixed the problem long since then, even though he sometimes still tests me. I have 4 ways to help fix it:
1. If you NEED to get him out asap, like for the vet/emergency/etc, just bring a big bucket of grain out. When my horse knocked his hip running from me, we gave in and brought food so we could look at the wound he gave himself. Sure, he won that round, but there will be plenty of other times to win yourself.
2. If your horse is a runner, that runs away from being caught, turn the "fun" into work. Make him run. And run. And run. Eventually you will get that inner ear turned to you, and you will get signs of him wanting to come in to you. I always add one or two laps after I see the signs, just to make sure.
3. If he likes to walk/trot away, turn your back to him when he starts moving. As soon as he takes one step of walk/trot, turn your back to him. It takes the "fire" away, so to speak. It also takes the fun out of the game.
4. If he is in a relatively small pasture, choose a point to walk to, and go to it. Completely ignore what your horse is doing, and walk to the opposite side of the fence. Turn a different direction, and continue. Soon, make your lines closer and closer to him. If he is anything like my horse, he will watch you like you are stupid. My horse stands there absolutely baffled at what his crazy owner is doing this time.
As soon as I would catch my horse, I would have a treat in hand. They will want to come up to you for a little something good. I always, always before I ride take my time grooming him, to give him something pleasurable, so it's not all about work. Or some days, I catch him and just walk and let him graze. All horses deserve a little bit of a break from work for a little fun day.
After 5 years of looking for the right answer to my horse that didn't want to be caught, he finally comes up to me in the pasture. I combined all 4 of those methods, using different ones at different times. Now my horse either walks or trots up to me, and shoves his nose into the halter, ready for work.
As for the not wanting to walk, bring a nice, longer lead out with you. I think mine is like 20 ft. I would say, don't bring your usual lunge line, or else your horse will get the idea of work. Having a longer line on his halter will give you the ability to do some real ground work in the pasture, instead of being limited to a shorter one. If he doesn't want to move, back him up/move his shoulders/move his hips/do circles with a lot of direction changes/etc. Make the work be in the pasture. After a few session of not having fun in the pasture, I bet he will want to walk with you and avoid all of the unnecessary work all together.
I hope some of this will work! Best of luck!