Most of the semps with red color/pigment in them will turn dark red during the winter. The ones without red will go darker green during winter. This is a generalization but holds mostly true. Semps that are bright green or can do yellow, will go their most yellow during the spring when there is abundant moisture and they are growing at their most rapid rate. Never much noticed what the blues and grays do during those seasons, so I will have to track that down.
So to answer your question, a red arachnoidem would have dark red color and white webbing on it during the Christmas season. There's a small, red arach out there called "Red Cobweb" that gets to be about 1". That might be one you are looking for. Can't say for sure as mine are usually covered by snow then.