First, apologies to david1976 for adopting his recent thread:
I had a similar problem with the stock on my Tikka M55 - out in the snow a few times, it was looking a bit sorry for itself. I read the above thread with interest, and had an exchange of pms with two of the contributors - "olaf" and "simjim33 (aka Fusion Stock Works)" - many thanks both for all your help and encouragement!
Like david1976 I decided to use olaf's procedure for cleaning and oiling the stock: clean with a mixture of equal parts methylated spirits/turpentine (substitute)/raw linseed oil; treat with 80:20 raw linseed oil/turpentine (substitute) once daily for a week, once a week for a month, once a month for a year, then as necessary thereafter!
I'm currently halfway through the "once a week for a month" stage, and I think it's looking encouraging. I've attached one picture taken before I started and some of how it looks so far (hopefully you can tell which is which!). I'll definitely be completing the process.
Once again, many thanks to olaf and simjim33.