Large horns or antlers require a high energy allocation to produce and carry both physiological and social reproductive costs. Following the principle of energy allocation that implies trade-offs among fitness components, growing large weapons early in life should thus reduce future growth and survival. Evidence for such costs is ambiguous, however, partly because individual heterogeneity can counterbalance trade-offs. Individuals with larger horns or antlers may be of better quality and thus have a greater capacity to survive. We investigated trade-offs between male early horn growth and future horn growth, baseline mortality, onset of actuarial senescence, and rate of ageing in an Alpine ibex (Capra ibex ibex) population. Horn growth of males in early life was positively correlated to their horn length throughout their entire life. Cohort variation and individual heterogeneity both accounted for among-individual variation in horn length, suggesting both long-lasting effects of early life conditions and individual-specific horn growth trajectories. Early horn growth did not influence annual survival until 12 years of age, indicating that males do not invest in horn growth at survival costs over most of their lifetime. However, males with fast-growing horns early in life tended to have lower survival at very old ages. Individual heterogeneity, along with the particular life-history tactic of male ibex (weak participation to the rut until an old age after which they burn out in high mating investment), are likely to explain why the expected trade-off between horn growth and survival does not show up, at least until very old ages.