Years back I'd a complete domain/host in wordpress and that i could change things i want. However I am exploring free wordpress host. Every existing blog theme includes a title within the page top, however i desired to put a small logo design before that, is it feasible in freehost wordpress?

I have already clarified a question about Wordpress. I believe here you will not have any obvious answer as with stackexchange for "wordpressers". Try here: http://wordpress.stackexchange.com/

For your question, I believe you cannot get it done.

Glad to assist