Natural language interfaces (NLIs) have become a prevalent medium for conducting visual data analysis, enabling people with varying levels of analytic experience to ask questions of and interact with their data. While there have been notable improvements with respect to language understanding capabilities in these systems, fundamental user experience and interaction challenges including the lack of analytic guidance (i.e., knowing what aspects of the data to consider) and discoverability of natural language input (i.e., knowing how to phrase input utterances) persist. To address these challenges, we investigate utterance recommendations that contextually provide analytic guidance by suggesting data features (e.g., attributes, values, trends) while implicitly making users aware of the types of phrasings that an NLI supports. We present SNOWY, a prototype system that generates and recommends utterances for visual analysis based on a combination of data interestingness metrics and language pragmatics. Through a preliminary user study, we found that utterance recommendations in SNOWY support conversational visual analysis by guiding the participants' analytic workflows and making them aware of the system's language interpretation capabilities. Based on the feedback and observations from the study, we discuss potential implications and considerations for incorporating recommendations in future NLIs for visual analysis.