Is one permitted to shovel on Shabbat if there is so much snow that he cant get to shul unless he shovels his way?
Yes, this is permitted.
This applies where there is an eruv or in a private domain, where there is no concern for carrying.
There are a number of halachic issues concerning snow on Shabbos.
The main consideration will be the question of mukzeh.
On this issue see Shulchan Aruch 320:9 where we see that snow is not mukzeh. This also emerges from the Shulchan Aruch in Siman 338:8, and the Mishnah Berurah explains that the problem of nolad does not apply to rain – the same apparently being true of snow. See also Shut Har Zvi, Kuntress on 39 Melachos, Soter. Although Rav Moshe Feinstein is stringent (Iggros Moshe Orach Chaim 5:23), most authorities are lenient.
Yet, even Rav Moshe will agree that it is permitted to shovel snow, since the snow is not being moved directly but indirectly (by the shovel). For this matter see Taz (308:18) concerning moving bones off the table with a knife, and see Mishnah Berurah 308:115 (though see Shulchan Aruch HaRav 308:60 and Chayei Adam 67:6, and see Chazon Ish 47:14).
Moreover, the Rema (308:6) writes that it is permitted to move broken glass because this is a hazard, and the same will apply here (though it can be argued that the person can simply stay at home – yet based on the considerations above, one does not need to be stringent).
Some have also discussed the matter of “destruction” and the issue of exertion on Shabbos (see here), but these considerations are not sufficient concern for stringency in this matter.