Show jumping is one of the most popular equestrian disciplines although strategic jumping per se is seldom used by free-living horses when negotiating obstacles that they might otherwise avoid. To establish if horses are naturally motivated to jump, we examined horses in a free-choice situation when negotiating various obstacles under test conditions. Eighteen leisure horses (LHs) and 16 sport horses (SHs) participated in a number of 2-choice tests. First, horses were presented with 2 optional routes during a “free-choice test” to reach a food stimulus. The choices were a shorter route (over an obstacle) or a longer route (around the obstacle). During 8 consecutive trials, the horses encountered an increase in obstacle height on every second trial as follows: 0, 20, 35, and 50 cm. In the “ridden test” after an initial conditioning period, the horses were tested with a Y-maze formation during 3 consecutive trials, where one element of the maze contained an obstacle arm (OA). The horses walked or trotted over the obstacle most frequently (59.9%) and jumped the obstacle in only 10.7% of the cases. For both the LH and SH groups, the horses' motivation to traverse the obstacle decreased as the obstacle height increased and only 44.1% of horses actually negotiated the 50-cm obstacle as compared with the 20-cm obstacle (85.3%). The LH group preferred to go around the obstacle significantly more often than the SH group (24 trials, 16.7% vs. 9 trials, 7.0%, for SH and LH, respectively; χ2 = 6.81, N = 33, P = 0.0090). The LH group used a jumping strategy to clear the obstacle far less frequently (6 trials, 4.2%) than the SH group (23 trials, 18.0%; χ2 = 9.96, N = 29, P = 0.0023). In the Y-maze trials, the LH group exhibited preference (40 per 54 trials, 74.1%; χ2 = 12.5, P < 0.0001), and the SH group failed to exhibit any preference (20 per 48 trials; χ2 = 1.33, P = 0.3123). There was no evidence of any correlation between the motivation to clear the obstacle and total number of OA choices in either the LH group (rs = 0.13, P = 0.9594) or the SH group (rs = −0.25, P = 0.3492). The findings from the present study indicate that SHs are motivated and willing to jump obstacles more often than are LHs under similar conditions. However, the apparent reluctance of the horses overall to continue jumping as the obstacle height increases suggests that, in general, many horses could easily encounter excessive demands (overfacing) in sport. This issue should be carefully monitored in terms of equine training, competition, and welfare.