Rising mental health issues among youth have increased interest in automated approaches for detecting early signs of psychological distress in digital text. One key focus is the identification of cognitive distortions, irrational thought patterns that have a role in aggravating mental distress. Early detection of these distortions may enable timely, low-cost interventions. While prior work has focused on English clinical data, we present the first in-depth study of cross-lingual and cross-register generalization of cognitive distortion detection, analyzing forum posts written by Dutch adolescents. Our findings show that while changes in language and writing style can significantly affect model performance, domain adaptation methods show the most promise.