From LA Lake Arrowhead would have a lower probability of having snow. http://www.geocaching.com/map/default.aspx?lat=34.25113&lng=-117.18917
Including a geocaching map of Lake Arrowhead. Rt. 173 down from the "Rim of the World" looks like fun.

I 've to both areas numerous times. I think Big Bear has a cute, funky little downtown. And there is a nice trail, that is maintained by the city or some governmental agency, within the city limits.

However, I think Lake Arrowhead is prettier and closer to those driving in from LA.

Take a look at Idyllwild, on Mt. San Jacinto. I think it's prettier than either of the other two.

The only problem with Idyllwild, is the drive up the mountain. It winds back & forth and the drive seems to take forever! It is a fun spot to visit though.

I like all three areas for different reasons. Lake Arrowhead Village is a great day trip that is easy to drive and fun to do for brunch or lunch. We especially like Belgium Waffle Works. They have sight seeing boats that run in the summer. There are also some quaint bed and breakfasts like Fleur du Lac and Rose Gables. One was supposed to be a mountain hangout for Bugusy Siegal, even boasting a lady ghost but I think it is closed now.
Big Bear is great for activity - skiing, snow boarding, cross country, sledding, shopping in town, hiking, fishing, boating, horse back riding, etc. It is a bigger town and has several lodges and restaurants. Having a thing for b and b's, I like Apples Bed and Breakfast.
But my favorite of the three is Idlywild. It isn't as high and usually doesn't have as much snow (or as much black ice in the winter) but it has a quiet small town charm that I can go back to over and over. Bread Basket, Red Kettle, the Gastrognome, and Arriba are favorite eating spots. Strawberry Creek Inn has a lovely spot by a little creek within walking distance of the town. The Visitors Center has several hiking trails, ranging from an easy walk to more of a workout, and you can go through the indoor displays before you go so you know what birds or animals you might see. Lake Fulmore has swimming and nice picnic areas. Lily Rock towers above town calling to rock climbers and story tellers. I love that you can see Catalina from the peaks on a clear day. I think Idlywild seems to be more pet friendly too.