The answer to your question would be that the figure of speech that describes winter as an old man with a white, frosty beard is personification. Personification is a figure of speech in which an idea or an animal is assigned human characteristics.
Then, the figure of speech used in the expression "happy as a lark" is a simile. A simile is a figure of speech that makes a comparison between two different things. It is a direct comparison because it draws resemblance with the words "as" and "like".