The tree pattern matching problem is, given two labeled trees P and T, respectively called pattern tree and target tree, to find all occurrences of P within T. Many studies have been undertaken on this problem for both the cases of ordered and unordered trees. To realize flexible matching, a kind of variable-length-don't-care's (VLDC's) have been introduced. In particular, the path-VLDC's appear in XPath, a language for addressing parts of an XML document. In this paper, we introduce horizontal VLDC's, each matches a sequence of trees whose root nodes are consecutive siblings in ordered trees. We address the tree pattern matching problem for patterns with horizontal VLDC's, In our setting, the target tree is given as a tagged sequence such as XML data stream. We present an algorithm that solves the problem in O(mn) time using O(mh) space, where m and n are the sizes of P and T, respectively, and h is the height of T. We adopt the bit-parallel technique to obtain a practically fast algorithm.