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Style transfer has achieved great success and attracted a wide range of attention from both academic and industrial communities due to its flexible application scenarios. However, the dependence on a pretty large VGG-based autoencoder leads to existing style transfer models having high parameter complexities, which limits their applications on resource-constrained devices. Compared with many other tasks, the compression of style transfer models has been less explored. Recently, the lottery ticket hypothesis (LTH) has shown great potential in finding extremely sparse matching subnetworks which can achieve on par or even better performance than the original full networks when trained in isolation. In this work, we for the first time perform an empirical study to verify whether such trainable matching subnetworks also exist in style transfer models. Specifically, we take two most popular style transfer models, i.e., AdaIN and SANet, as the main testbeds, which represent global and local transformation based style transfer methods respectively. We carry out extensive experiments and comprehensive analysis, and draw the following conclusions. (1) Compared with fixing the VGG encoder, style transfer models can benefit more from training the whole network together. (2) Using iterative magnitude pruning, we find the matching subnetworks at 89.2% sparsity in AdaIN and 73.7% sparsity in SANet, which demonstrates that style transfer models can play lottery tickets too. (3) The feature transformation module should also be pruned to obtain a much sparser model without affecting the existence and quality of the matching subnetworks. (4) Besides AdaIN and SANet, other models such as LST, MANet, AdaAttN and MCCNet can also play lottery tickets, which shows that LTH can be generalized to various style transfer models.