Although horses are social animals they are often housed individually with limited social contact to other horses and this may compromise their welfare. The present study included eight young female horses and investigated the strength of motivation for access to full social contact, head contact and muzzle contact, respectively, to a familiar companion horse. Horses were housed individually next to their companion horse and separations between pens prevented physical contact. During daily test sessions horses were brought to a test area where they could access an arena allowing social contact. Arena access during 3 min was given after completion of a predetermined number of responses on a panel. Fixed ratios (FR) of 8, 16, 24, 32 and 40 responses per arena access were applied in a random order, one per daily test session, within each test week (Monday to Friday), and the number of rewards per daily test session was recorded. All horses could access all three types of social contact in a cross-over design, and an empty arena was used as control. Motivational strength was assessed using elasticity of demand functions, which were estimated based on the number of rewards earned and FR. Elasticities of demand for the three types of social contact were low (−0.20), and not significantly different, although increasing FR still resulted in a decrease in rewards obtained for all three types of social contact (P < 0.001). Across FRlevels horses earned more rewards for social contact than for an empty arena, as shown by much higher intercept values (2.51 vs. 0.99; P < 0.001). However, the elasticity of demand for infrequent access to an empty arena (−0.08) was lower than for social contact (P < 0.01) and not significantly different from zero (P = 0.07). Horses performed more social behaviour the lesser the restriction on social contact (full > head > muzzle). However, the finding that horses showed a similar and high motivation for all three types of social contact suggests that they are valued equally highly in a situation where the alternative is no social contact.