Town Faire is a reputable business.  What did they quote you to repair?  Can you sleep at night with that cost?  If not locate a second opinion.  Maybe a trusted mechanic. 

Your axel weight ratings should be on the VIN tag.  You can call the manufacturer of the trailer and find out what type of axels and hubs along with many other specs to that axel.  Then Google away to get a general idea of your parts costs.

Most everything is repairable and replaceable.  Greese seals and brake shoes are affordable.  No need to think you need a whole new axel.  But be carefull I would not haul my horses before I got a second opinion. 

The technician had to pull your brake drum to inspect your brakes.  He may have remove the grease cap, axle grease can be pink and he may have laid it inside the cap to keep it clean durring the inspection.

To pull the brake drum, repack a wheel bearing and install a new grease seal takes about a half an hour. The grease seal is typically < $5. The brake shoe retainers could need replacing or the whole brake shoe assembly and springs may need changing. This will not be evident until the drum is pulled. A complete brake assy can be changed in less than 20 mins once the drum is removed.

As was previously posted, you do not need a new axle. Nor was there any reason for the axle nut to be removed, when pulling the wheels whilst changing the tires.

The grease seal is on the inside of the brake drum, a location not visible while changing a tire. Normally this area would not be scrutinized during the course of a tire change. When the drum is pulled, a failure would be indicated by a radial display of grease, emanating from the center and spreading to the outer extremes. Any excess grease will be spread on the inside of the drum and brake shoes.

It is possible that when the  mechanic removed the tire and wheel, the brake drum rotated and he heard a shoe dragging inside the drum. The shoes can be adjusted through the backing plate, and properly seated against the drum. If they are adjusted and still make a noise, one or both shoes could have missing or broken retainers, allowing them to lay against the drum.

The mechanic could be on the ball and discovered a legitimate maintenance issue, or he is prescribing unnecessary repairs to enhance his wallet.

Since this is an older trailer that has not been used in a year... You'll be well served to have all 4? wheel bearings repacked and the grease seals replaced.  When the wheel hubs are removed to repack the bearings,  The brakes, bearings, magnets, etc can be inspected and repaired/replaced as required.  That is your best option for safety and reliability.

This may sound dumb but when was the last time you had the wheel bearings packed?  How about the last time the brakes were checked?  These are maintenance issues I have done every spring before I start my long weekend hauls.  You say nothing felt wrong.  I can't take the chance on waiting to "feel" if something goes wrong with my horses on board.  I have gained alot of information on this forum and one thing is to have the yearly inspections done. The technician/mechanic is probably saving you a major headache by pointing out these things now.  The brakes could lock up on you while you are a great distance from home with horses on board.  Think how much that would cost to have your trailer towed and someone to come haul your horses back home.  Think if you lost control of the rig while it happened.  The mechanic may have sensed you didn't want to put alot of money in it and "offered" to do it on the side saving you probably half the cost by paying him cash.  It happens all the time.  That doesn't make him a crook or trying to get over on you.  What you need to look into is getting an annual inspection of your trailer from a qualified mechanic.  Check all the lights, brake box battery, flooring, pull the wheels and check the brakes, wheel bearings, fittings.  It usually costs me $75 - $100 to inspect and pack the bearings.  I'm not trying to get down on you, just trying to make it real that these things have to be done to keep everyone safe.