I just found a section on the Solr wiki where they describe this exact feature for release 4.4 (which is not released yet).
It does have some prerequisite configuration on the Solr instance, but it does allow you to add fields to the schema. Based on that information, I can't see why they won't eventually extend the functionality to allow you to delete as well. I guess we will have to wait and see.
Here is the link to that section: http://wiki.apache.org/solr/SchemaRESTAPI#Adding_fields_to_a_schema. It also references this JIRA issue: "In preparation for dynamic schema modification via REST API, add a "managed" schema facility".