So, on the front it's basically a stalemate with constant shelling by artillery? What is this, WW1?
No, it's a semi-frozen conflict. There are many of those around Russia due to them trying to police all of the ex-USSR countries, the hottest one outside of Ukraine is probably in between Armenia and Azerbaijan. They've actually used attack helicopters there in the latest bout of hostilities, IIRC.
I think you mean a Cold War? Because semi-frozen would be cold. Though obviously the US and USSR didn't skirmish with each other.
Actually, it sort of lies in the region between a full on Cold War and a hot war with major fighting. maybe.
A frozen conflict is a war or previously-active military conflict that's not actively moving in either direction, but which hasn't been concluded by a peace treaty or other conclusive diplomatic arrangement. A cold war is one in which direct military engagement is not being pursued, but one in which the primary means of conflict are economic, political, social (propaganda), espionage, and/or proxy conflicts between third-parties. Not all frozen conflicts are cold wars, and not all cold wars are frozen conflicts. For instance, the most famous Cold War between the US and USSR was not a frozen conflict; there was never an active military state of war between the two powers. The war between the ROC and PRC is frozen, but is not a cold war as, occasional rhetoric aside, the two have largely adopted a "live and let live" attitude as long as the present status quo holds. The two Koreas are both.
EDIT: Actually, it just occurred to me that the present circumstances between Japan and Russia are an even better example of a frozen conflict that isn't a cold war, at least in legal terms. Due to the disputes over the Kurils and Sakhalin, Japan and the USSR never signed a permanent peace treaty, a state carried over to the latter's successor state post-1991. This state of permanent legal ceasefire has persisted even after the 1950s normalization of relations, the Gorbachev thaw, and the utter collapse of the Soviet state. Indeed, it's so frozen that most don't even know it still exists under all that ice.