Methods are disclosed for fabricating heat exchangers and Heat Exchanger (HX) tubes, as are heat exchangers fabricated in accordance with such methods. In embodiments, the method includes the steps or processes of obtaining a Non-Equilibrium Alloy (NEA) feedstock powder comprised of an alloy matrix throughout which at least one minority constituent is dispersed. The first minority constituent precipitates from the alloy matrix when the NEA feedstock powder is exposed to temperatures exceeding a critical temperature threshold (TCRITICAL) for a predetermined time period. A cold spray process is carried-out to at least partially form the HX tubes from the NEA feedstock powder; and the HX tubes are subsequently installed in the heat exchanger. The HX tubes are exposed to a maximum temperature (TSPRAY_MAX) during the cold spray process, which is maintained below TCRITICAL to substantially preserve the non-equilibrium state of the NEA feedstock powder through cold spray deposition.