Can you install a steel beam in timber posts?
You have several issues to consider: 1) span of steel beam vrs. wood beam, 2) weight of steel beam vrs. wood beam, 3) connectors, 4) ease of connecting joists to wood beam vrs. steel beam, 5) ease of installing wood post vrs. steel post, 6) size of footing under posts. 

1) Yes, steel beams can be smaller than wood beams when carrying the same load and spanning the same distance. However, if there is a headroom problem, you can move the beam up and have the joists frame into the side of the beam or reduce the span of the wood. 

2) Physically moving the beam into place is going to be difficult. A steel beam may weigh less, but with a wood beam you can nail supports to the side of it to keep it level, aligned, stable, etc. Also, if the beam needs to be cut to fit, wood is easier. 

3) Connectors from a steel beam to a wood post will need to be custom and probably designed by a structural engineer. However, a connector from a wood beam to a wood (or steel) post is readily available and standard through Simpson Strong Tie. (See Simpson LCC or CCOS connectors for wood to steel posts.) See here: https://www.fastenersplus.com/shop-by-product/simpson-connectors/post-bases-post-caps/lccccos-lally-column-caps

4) Connections from wood joists to steel beam is not standard and you’ll need a structural engineer to determine ledger size and bolting, plate size and bolting, etc. Whereas wood to wood Connection is standard. 

5) When wood posts are cut to fit, they must be the perfect length. Fitting a wood post with a connector on it is very difficult to “pound” into place and fit tight. However, using a “Lally Column” allows adjusting in place. 

6) If you are trying to span an extra long distance by using a steel beam, your footing will need to be extra large too. Make sure it’s sized properly. 

Summary:
Generally for ease of construction, the beam and posts are reversed: wood beam and steel posts.