The Tundra is a 1/2 ton truck. My personal opinion is they make a great daily driver, excellent to chase to Home Depot and pick up bedding plants for the yard or drop the lawn mower off at the repair shop, run your son to ball practice with a couple bags of team equipment in the bed. But they are not a serious tow vehicle.

The 2010 Tundra has a rated payload of 1385lbs when equiped with a tow package.  Subtract a Driver and passenger (2x150lbs) and your effect payload is 1085 lbs. Install a B&W Turnover ball for your Gooseneck Hitch and Subtract another 100lbs leaving you 985lbs of payload.  I don't know of any Gooseneck trailers that have that light of a pin weight.

The truck is rated to tow a 8100 lb trailer. Most Gooseneck trailers have 25% of the trailer weight on the Pin or Ball. So a trailer weighing 8100 * 25% =2025lbs which is double what the tundra has available.

So while the truck probably has enough power in the engine to pull a smaller Gooseneck trailer. It just doesn't have the load capacity to carry a Gooseneck trailers Pin weight.

http://www.toyota.com/tundra/specs.html

Bottom line you need to get any trailer you are considering weighed and make the dcecision based on that weight

Paintedhorse has offered good GN info.

You should also consider the nose width of the trailer and the bed of your Tundra.  Short beds and wide noses aren't compatible with sharp turns.

Also consider the neck-over height of the trailer vs the bed height of your Tundra.  Road dips and other uneven road heights can cause your truck bed rails and the bottom of the GN to contact.

BP keep more of the trailer weight on the trailer tires.  They transfer less to the hitch. In your case probably 600-800 lbs. So they don't affect the load capacity of the truck as much as a GN. But a BN is more stable since it does transfer weight to the truck and even more important, That weight is up over the axle, not hanging on the bumper.

Even if the GN trailer you are considering is 3700 lbs, add in a spare tire, some basic tools, your saddles and tack, maybe a bag of feed, and you are easily 4500lbs.  Load two horses and now you are 6500 lbs. Thats still putting 1600 lbs on the bed, and that is more the Payload its rated for.

So I think you would be safer pulling a BP with that truck. But I would still weigh it and make sure what you weigh when you are all loaded and hooked up.

Some BP trailers have their axles far to the rear of the trailer. If you add any kind of DR to the front, you will end up with a great deal of hitch weight on the bumper. This weight, being behind any direct suspension support, will greatly effect the truck's handling, load capacity and suspension.

Many times the only corrective options are to install suspension assists and WD accessories to the hitch assembly. By carefully shopping for trailers with the axles mounted forward under the stalls, you can reduce the tongue weight over similarly sized units.

I'm new here but gonna throw in my 2 cents.  I have a Tundra 5.7L double cab with tow package.  Installing the tow package took the payload from 1600lbs to 1450lbs.  I had a Roadmaster Action Suspension system installed to help support my truck bed in general - hauling dirt, trailers, etc.  It's claim was increased payload 25-40%, control "dolphining" and sway.  I didn't have any real problems before it was installed but definitely is quieter pulling with the RAS, particularly over wavy bridges.  I also use weight distribution bars.  If you're looking at 2H BP w/DR, the Tundra works fine.  I had originally pulled it with an older Tundra 4.8L I think, same experience.

I've hauled that rig all over the Mid-Atlantic region to various organized weekend trail events (highways, bridges, tunnels, mountains).

Meanwhile, I've outgrown the BP (sick of tenting it) and moving to a new, all aluminum, empty wt 3800lb GN, about 950 tongue wt.  I pull 2 horses (2100lbs) and I'm planning to be diligent about keeping things under 7000lbs loaded.  I've done a lot of research, measuring and feel confident about getting a 2H slant GN.  A GN and Tundra can be done, you just have to do a lot of fact finding and stick to a 2H rig.

Good luck today Betsy! 

Although one can find many knowledgeable dealers, I would ask for a spec sheet and confirm the empty weight.  They don't put it on trailer labels because the minute you add any options, it becomes inaccurate.  I've found most 2H GN's are around 7500lbs GWVR.  As for the gooseneck, almost every manufacturer makes the new ones tapered enough to avoid any back window and turning troubles.  I think you'll find about 42" of turning clearance (trailer stem to back window).  It's scary close but works!

I found for my application that 3800lbs was my limit because of options, horse, hay, water, tack and personal gear loads.  Depending on your horse size(s) you should probably keep empty weight under 4000lbs when pulling with your Tundra.