You can get a straight cut in soft felt by compressing it evenly before
you cut it.  Cut a narrow slot in a block of wood plastic or metal that
is as narrow as you can make it, just enough to fit a razor blade into.
The idea is to hold the felt on both sides of the cut and to guide the
blade perfectly straight.

Press down on the felt with the block and make sure you do not twist it
or press down unevenly.  Then cut with a razor blade or a scalpel.  It
should be a sharp one and you will want to replace it often if it is a
typical single edge blade.  Most are terrible today as they are utility
blades which are not made for shaving.  You can still get single edge
shaving quality blades and you can also use double edge ones but it is
easy to cut yourself with them.

All fine felt is made by a controlled process of heating and cooling to
obtain the desired properties.  I don't think it would be a good idea
to wet it and freeze it.

You can also sew felt just as it was done originally.  I have done this
but it is a little tricky because the felt wants to compress unevenly.
It is easier to do if you glue it to a strip of woven felt first so you
can put all the pieces in a row, nicely packed together.  I used a
commercial sewing machine.  It would probably be difficult to do a good
job on a typical light weight domestic machine.

There is also a tool that used to be available from piano supplies that
did essentially the same thing.  I think they still might be available.

Best regards,
Spencer Chase
Garberville, CA
http://www.spencerserolls.com/