Sleepy drivers have problems with keeping the vehicle within the lines, and might often need to apply a sudden or hard corrective steering wheel movement. Such movements, if they occur while driving on a slippery road, might increase the risk of ending off road due to the unforgiving nature of slippery roads. We tested this hypothesis. Twelve young men participated in a driving simulator experiment with two counterbalanced conditions; dry versus slippery road x day (alert) versus night (sleepy) driving. The participants drove 52.5 km on a monotonous two-lane highway and rated their sleepiness seven times using the Karolinska Sleepiness Scale. Blink durations were extracted from an electrooculogram. The standard deviation of lateral position and the smoothness of steering events were measures of driving performance. Each outcome variable was analysed with mixed-effect models with road condition, time-of-day and time-on-task as predictors. The Karolinska Sleepiness Scale increased with time-on-task (p < 0.001) and was higher during night drives (p < 0.001), with a three-way interaction suggesting a small increased sleepiness with driving time at night with slippery road conditions (p = 0.012). Blink durations increased with time-on-task (p < 0.01) with an interaction between time-of-day and road condition (p = 0.040) such that physiological sleepiness was lower for sleep-deprived participants in demanding road conditions. The standard deviation of lateral position increased with time-on-task (p = 0.026); however, during night driving it was lower on a slippery road (p = 0.025). The results indicate that driving in demanding road condition (i.e. slippery road) might further exhaust already sleepy drivers, although this is not clearly reflected in driving performance.