A good deal of evidence links leukoaraiosis (white matter lesions or WML) to decline in executive function and there is much evidence linking WML to hypertension.
Here is a recent paper linking non-amnestic mild cognitive impairment(MCI) to hypertension.
A number of cross-sectional studies linked hypertension with WML, here is one prospective study showing the same findings increasing the weight of the evidence of the association.
The periventircular WMLs seem to correlative with frontal lobe dysfunction ( such as diminution in executive function) and also with abnormalities of gait. In fact, a paper from the Bronx Aging study published in NEJM showed a clear relationship between the development of a "frontal lobe" type gait and the subsequent appearance of a vascular type dementia with relatively good retention of verbal memory skills but much difficulty in executive function. The widely used Mini-Mental status is not a great tool for detection of the "hypo-frontal" patient. Watching the patient walk can give valuable information about the elderly patient whose mental status has become an issue.