I reported this, but I think, with context, this sentence could work. In isolation, it's extremely awkward however.
Alternatives: We like Spring. We like the Spring months, We like the season of Spring
The plural of spring is spring, unless referring that different types of spring. E.g I like all of the springs in the countries around Europe. PS ... there doesn’t appear to be a reason, but seasons are not proper nouns, and hence, are not capitalised.