Cross-domain cold-start recommendation is an increasingly emerging issue for recommender systems. Existing works mainly focus on solving either cross-domain user recommendation or cold-start content recommendation. However, when a new domain evolves at its early stage, it has potential users similar to the source domain but with much fewer interactions. It is critical to learn a user's preference from the source domain and transfer it into the target domain, especially on the newly arriving contents with limited user feedback. To bridge this gap, we propose a self-trained Cross-dOmain User Preference LEarning (COUPLE) framework, targeting cold-start recommendation with various semantic tags, such as attributes of items or genres of videos. More specifically, we consider three levels of preferences, including user history, user content and user group to provide reliable recommendation. With user history represented by a domain-aware sequential model, a frequency encoder is applied to the underlying tags for user content preference learning. Then, a hierarchical memory tree with orthogonal node representation is proposed to further generalize user group preference across domains. The whole framework updates in a contrastive way with a First-In-First-Out (FIFO) queue to obtain more distinctive representations. Extensive experiments on two datasets demonstrate the efficiency of COUPLE in both user and content cold-start situations. By deploying an online A/B test for a week, we show that the Click-Through-Rate (CTR) of COUPLE is superior to other baselines used on Taobao APP. Now the method is serving online for the cross-domain cold micro-video recommendation.