Eleanor Kellon, VMD
What you do with it depends on your goal. The high dose is for weight loss. You are creating an abnormal hyperthyroid state with it. This will also suppress the horse's normal thyroid function which is why you should gradually wean off, giving the thyroid time to kick back in.
Many horses with EMS, PPID, obesity or any chronic condition will have low T4. It's probably euthyroid sick syndrome https://www.merckmanuals.com/professional/endocrine-and-metabolic-disorders/thyroid-disorders/euthyroid-sick-syndrome because they respond normally to TSH but since we can't test TSH or rT3 that's not able to be confirmed.
When the diet is balanced and the underlying condition controlled, thyroid function usually returns to normal. Some vets advise to use lower doses of Thyro-L, just enough to bring T4 back to normal, especially when the horse is dull and depressed. This is a much more conservative approach but not necessary in the end.
Eleanor in PA