Well, if you really plan to take it all the way to round-n-shiny
then you need more than schematic editing, you need things
like at minimum a SPICE netlist export (preferably an integrated
layout and verification tool - SPICE:SPICE LVS can give you a
thumbs up / thumbs down but is not too debug-friendly).
The LASI system is kinda cute, has schematic, layout, SPICE
export from either, DRC, etc. There are some MOSIS processes
supported, perhaps they have added new ones since I last
looked.
Electric is another good suite, it's not useful to me because
my needs often involve GDS-II import and the data structure
of Electric uses constructs that can't be made from GDS-II,
only the "forward path" of direct layout editing. But a fairly
complete tool as long as you're working entirely within it.
You will have to compile it yourself if you don't want to pay
for object-code on media, source is free.
Several open-source schematic editors with SPICE export.
Where you'd get the models and device library, is a problem.
I'd look into gEDA and the side branch links you may find.
Silvaco and Tanner are tools you'd pay for but are on the
affordable end and have some decent level of foundry
support (PDKs).
I know old-timers who still design ICs using antique PC
based tools, and work with foundries that still let you
tape-in against a groundrule package rather than insisting
on a Cadence PDK verification. These are getting fewer....
Teh Googlez probably would cough up a few million hits
for "free CAD schematic", if you have time to kill. There
are sites that try to keep track but staleness can be a
bit annoying.