Nope! You are not too heavy at all! 150-160lbs is not that heavy for an adult rider, especially one of your height. The average man weighs at least that much! It is true that some drafts are not quite as well suited for carrying weight on their backs as some riding horses, but it has more to do with their conformation than their size. There are plenty of Quarter Horses out there that are poor candidates for weight bearing.
If you are concerned about weight bearing and you plan to jump, you should look for horses that have good conformation through the legs. The horse should have short pasterns and canon bones that are large in circumference. The cannon bones should be shorter than the forearms. Basically, you want a horse with a good solid leg that is proportionate to the rest of their body. Short pasterns and canon bones mean that the connective tissue in the lower leg that is most prone to injury is shorter and therefore less likely to be injured. You want a horse with a pastern angle that matches the angle of their shoulder. Pasterns that are too upright do not absorb enough shock and pasterns that are too sloped will allow the fetlock to hit the ground when the horse is galloping or landing off a jump. Pasterns that are too sloped can also lead to greater risk of injury to the tendons and ligaments that support the pastern. You also want a horse with a good hoof. A broad hoof with a solid hoof wall will help absorb some shock. Broader hooves and joint surfaces have a larger area for weight distribution and are better at keeping a horse sound through pulling, jumping, running, etc. This is why many warmblood breeders and registries like a horse with good "bone". You also want to avoid horses with long backs if you are concerned about weight bearing. Short, strong backs can carry more weight.
Here is a good resource for conformation: Drafts with Dots: February 2012
If you scroll down you will see many good explanations on conformation and good pictures to help you understand.
There is no reason any well built horse that is properly conditioned and gradually worked up the levels in jumping should sustain injury. People with little draft experience will tell you that drafts are just too big and if ridden or worked hard they will injure and be lame. Drafts are hardy animals that are worked hard in a rural setting for their entire adult lives and if treated properly, they can be sound and usable well into their twenties or even thirties, just like any other type of horse. Draft horses should have thick legs and broad hooves designed to carry their own weight. If so, there is no reason their own weight should be the death of them.
With that said, you have to keep in mind that draft horses are BIG. This doesn't mean they can't jump. It just means they will not be as light on their feet or maneuverable around courses as a lighter horses. Draft horses tend to be heavier on the forehand and you must work hard to get them off the forehand and using their haunch to get over your fences, and many draft horses will not pick up their feet neatly over a fence which is not good for hunters. They are just not as graceful and refined as other horses. This will show in your riding and performance, and you will have to work hard to overcome it. Hunter judges are also quite snobby at times so you may find yourself not placing no matter how hard you work or how well you show.
It is not true at all that all draft horses are lazy and have no impulsion. Many of them are very sluggish and do fit the "ho hum" draft personalty stereotype but this is certainly not true of all of them. Draft horses can be quite flashy and forward depending on the individual, and even a lazy draft can be trained to be lighter off the leg and move out when asked.
As a first horse, I would not recommend an unbroke or super young horse, of any breed. You may have some experience working with younger horses but it's a big commitment and learning curve when you finally own your first horse, and you should look for a horse that is at the right level for you. You want a horse that is not too much of a challenge for you, and doesn't present any obviously new training tasks for you to work through, but also shows potential in your desired discipline and presents enough of a challenge to keep you interested and learning for years to come. There's a delicate balance there. If you end up with too much of a challenge you will only become overwhelmed and frustrated and either have to sink a lot of money into professional training or sell the horse for another. Definitely invest in a horse that is mostly broke that you can work with and finish, and go for a greener horse next time you're horse shopping.
The best place to buy draft horses is anywhere you would buy any other horse. Look for horses for sale in your area on sites like dreamhorse.com, petfinder.com and equine.com. Since you're looking for a draft draftsforsale.com would be a good place to look. Always be wary of sellers that seem uneducated or dishonest, and always have any potential new horse evaluated by an experience friend or instructor and a veterinarian before making a final decision.
Too keep drafts cool in hot weather, keep their manes either trimmed or braided and excess body hair clipped. Provide them with shade and plenty of fresh water. Make sure you don't overfeed your draft or let them get too overweight, as this extra fat can hinder their ability to cool down. Many people will tell you that drafts eat A LOT, but this is not always true. Many of them are easy keepers and their weight should be monitored closely, just like any other type of horse.
Overall, for your riding goals, I would recommend a draft cross. You can have most of the qualities you love about a full draft in a slightly more refined and athletic package. I own a Shire/TB cross and she is wonderful! She is 17 hands and chunkier than a TB but lighter than a pure Shire. She's well built and well tempered. She is lazy at times but can be convinced to move out and moves with a more graceful, flat-kneed action like a TB. She has lovely form over fences and is praised by both of my instructors.