According to this LiveStrong article;
Living at or traveling to high altitudes can raise a person’s blood pressure, depending on the rate of ascent and the amount of time spent at the high altitude. The International Society of Mountain Medicine describes high altitude as 5,000 to 11,500 feet above sea level. At higher altitudes, the body works harder to process oxygen. This stress can cause high blood pressure. But the more time a person spends at the higher altitude, the better acclimatized the body becomes.
However, it also states that
"Prolonged exposure to high altitudes can have a positive effect on
hypertension, or high blood pressure. In his book "Medicine for
Mountaineering: And Other Wilderness Activities" Dr. James Wilkerson
writes that extended exposure to high altitudes may inhibit the
progression of hypertension in some hypertensive individuals. Dr.
Wilkerson also notes that many non-hypertensive individuals experience
the opposite effect, that is, an increase in blood pressure when
exposed to high altitudes."
Also, the Institute for Altitude Medicine state that
"Some persons with HBP, however, develop lower blood pressure on
ascent to high altitude."
In the November 2009 issue of the "Journal of Travel Medicine," Dr. Timothy O’Brien and colleagues reported on a study that found a group of black mountaineers experienced a drop in their systolic blood pressure numbers as they climbed to high altitude. Systolic pressure is the amount of force placed against the body’s arterial walls when the heart contracts. It is designated by the top number in a blood pressure reading. However, the systolic pressure of white mountain climbers increased as they ascended. The cause of the racial differences is unknown and may not apply to all individuals. The authors speculated that the observed differences seen in this small study may have been due to differences in genetics, hypoxic stress, diet and exercise.
Journeys to High Altitude—Risks and Recommendations for Travelers with Preexisting Medical Conditions (Kelly Mieske BSc Gerard Flaherty MB, MRCPI, MSc Timothy O'Brien MD, PhD) First published: 03 January 2010
There is a significant amount of individual variability in the effects of altitude on blood pressure. In the majority of people there is a small alpha adrenergic–mediated increase in blood pressure proportional to elevation gain,21 the effect of which is not clinically significant until above 3,000 m.2, 22, 23 However, in some people, there is a pathological reaction to high altitude which results in large blood pressure increases.5, 22 A work by Häsler and colleagues24 suggests racial differences in the blood pressure response to altitude