My view is that once a sign is installed, apart from an occasional wash down it should be left to weather to silver grey.
However, some items are best if it maintains a wood colour and this can be done using various products. Danish Oil, Linseed oil, OSMA oil are all suitable.
Please make sure that the product is not too old, thick and glutinous, otherwise the letters will hold too much oil and look unattractive.
For best results re oil before any streaks of grey weathering appear, approx every 6 months
Clean the sign first, wash and brush and allow to dry.
Brush oil on liberally all over and wait 10 minutes.
With a lint free cotton rag wipe off the excess oil.
Repeat as required.
For signs that are painted follow the above but wipe the oil off the painted surface straight away with a rag and white spirit. Return in 10 minutes to remove any drips of oil from below the letters.
Oak signs that have been supplied untreated can, in the first few weeks develop tears of tannin leaching out of the letters, especially after heavy rain.
Use a medium grit sandpaper (100) to remove these marks.
This will stop in time.
Do not use wire wool on oak outside, a blue stain will develop very quickly.