Learning is fundamentally linked to epinephrine, acetylcholin and dopamine.
Do heart pressure medication like beta blockers block these processes to some extent by reducing epinephrine?
Your question has the implicit assumption that beta-blockers prevent or impair the ability to learn new information. This is incorrect. There were a series of studies done in the 1980s addressing this topic. These were reviewed in an Archives of Internal Medicine (now JAMA Internal Medicine) study that concluded: "There is a suggestion in the literature that such agents [beta-blockers] may actually improve performance on complex tasks requiring well-controlled anxiety plus coordinated input from memory, perceptual motor functioning, and learning." Subsequent studies have looked at the effect of lipophilic beta-blockers like propranolol that can cross the blood-brain barrier and arrived at similar conclusions.
If your question was referring to memory consolidation during stressful situations, there's a recent meta-analysis that suggests that propranolol has limited utility in preventing traumatic memory reconsolidation.
Learning involves a complex system beyond the three neurotransmitters you've listed, one that is still being investigated. Complex systems can rarely be understood from first principles e.g. if X, then Y.