If you are using medications to control your hypertension, make sure you are fully aware of their side effects. In 2004 the American College of Sports Medicine wrote a full report on exercise guidelines for hypertensives. Included in the report were the following warnings for hypertensives on medications:

• Antihypertensive medications such as beta blockers and diuretics impair the ability to regulate body temperature during exercise in hot and/or humid environments
and provoke hypoglycemia (88,206). Thus, people using these medications should be educated on the signs/symptoms of heat illness, the role of adequate hydration, proper clothing to facilitate evaporative cooling, the optimal times of the day to exercise, the importance of decreasing the exercise dosage (time and intensity) during periods of increased heat or humidity, and methods to prevent hypoglycemia. In addition, beta blockers can substantially alter submaximal and maximal exercise capacity, particularly in those without myocardial ischemia and with nonselective
agents.
• Because antihypertensive agents such as alpha blockers, calcium channel blockers, and vasodilators may provoke hypotensive episodes after abrupt cessation of activity, extending the cool-down period is generally recommended (88,98).

Source:
“Exercise and Hypertension” This pronouncement was written for the American College of Sports Medicine by; Pescatello, Linda S. Ph.D., FACSM, (Co-Chair); Franklin, Barry A. Ph.D., FACSM, (Co-Chair); Fagard, Robert M.D., Ph.D. FACSM; Farquhar, William B. Ph.D.; Kelley, George A. D.A., FACSM; Ray, Chester A. Ph.D., FACSM. Medicine & Science in Sports & Exercise: March 2004 – Volume 36 – Issue 3 – pp 533-553. Special Communications. Can be viewed online at http://journals.lww.com/acsm-msse/Fulltext/2004/03000/Exercise_and_Hypertension.25.aspx