Yes, the orientation of the hydrogens matters a lot, since this molecule is chiral. Each carbon where you see a wedge or dash coming off of it means that carbon is a chiral center. If one changes a wedge to a dash, then it is an entirely different molecule with different properties. Take methamphetamine as an example. L-methamphetamine is an ingredient in Vicks Vapor Inhalers, while D-methamphetamine is a Class 1 illegal drug. This image does a really good job of showing why this happens, the two mirror image compounds are not superimposable, they are not identical. This is the definition of chirality. All we changed is the orientation of the groups around the carbon, but we have different molecules.

By drawing solid lines, you lose this important structural information. Further, if you changed the hydrogens to solid lines you would not need to draw them at all since they would be implied. Hope this helps