Will enclosing my porch keep my house warmer?
An enclosed porch can act as an oversized "storm window" for the part of the house it covers, so there is some insulation benefit. How much depends on how well the porch is air-sealed and insulated. It's probably a relatively small part of the surface of the house (unless it's a wrap-around porch), but it certainly won't hurt and, depending on prevailing winds and lighting conditions, might help.

An enclosed porch can also act as an "airlock", reducing how much warm air you lose each time you go in and out by preventing winds from blowing straight into the house. Again, probably not a huge effect, but it's there. And gives you a sheltered place to leave outdoor stuff like bicycles, or muddy shoes that you don't want to track into the house.

I doubt energy savings alone justify it. Those combined with increasing the year-round usefulness of the porch space might. 

(Mine just has storm windows all the way around. It definitely does work as windbreak and airlock and so on. Its R-value for the rest of the house is probably negligible, but I still find it useful -- and it gives me a screened porch in the summer as well. Someday I'll upgrade it into a three-season space, but there's no rush right now.)