If your neighbor has the trailer next door.  Walk over and get the weight off the trailer.  Better yet, throw a couple of horses in it and go find a scale and get the actual weight.  Both the total weight of the trailer and the actual Pin weight that will rest on the truck.

With those numbers you can look up your year of truck and see what it is rated to haul/tow  Run your truck across the scale and subtrack it's actual weight from the rating and see if your truck has capacity left that is equal to or greater than what the trailer weighed when you took it to the scale.

Look at where you tow and see just how tough the conditions will be. I might use a F150 at close to its maximum, if I was pulling on flat level terrain.  But if every trip was up and down big mountain passes. I'd sure be looking for a truck where my load would not be close to it's max.

In my opinion NO not at all!  Just like gard stated " empty" the truck might pull the trailer, but when you load horses and tack..... 

You maybe able to pull the trailer loaded but your question was "Would it be safe to pull ?".....  Plus you might check the engine size of the Dodge, if it is a 5.2L V/8 I would not even try and pull that trailer empty!

Depending on the amount you are saving it is possible to upgrade you truck. 

I would start with beefing up the transmission done by a reputable shop.   Following that replace the rear axle with an axle out of a 2500 or 3500 single rear wheel and if possible get an axle with disc brakes.  When you are getting axles get the springs that go with them. 

Doing all of that you will make your truck a ¾ ton with a ½ ton frame, as long as you don’t get too crazy with pin weight you will be okay with that set up as long as your frame does not have any rust, (surface rust is okay). 

Once all of that is done get E rated tires and enjoy your new trailer and truck. 

I have no idea what this will cost, but it can be done. 

What are you currently towing with those two trucks right now?  A 3 or 4 place steel bumper pull is almost the same weight empty as that featherlite GN. I'd much rather have the weight on a GN ball than on the bumper hitch.

Most of us in this forum don't like to tow much more than a light boat, an ATV trailer  or two place snowmobile trailer behind a 1/2 ton pick up. Those light duty pickups are really built to chase around with light loads. When you add 3 live 1200lb horses that move around as you drive, you jump from a light load to a heavy load.  So I would be just as leary of towing a 3h bumper pull as I would a 3H gooseneck trailer on a 1/2ton truck.  But if the actually weights fit into the rated load capacity and you are not in hilly or mountain area, maybe you can get by.

Personally I would go trade one of the trucks in and get a 3/4 ton or a 1 ton pickup to tow horses with. There are lots of used trucks around and the price difference from what you sell the 1/2 ton for and buy a similar model 3/4 ton just won't be that much.