What do mountains look like without precipitation? We have an excellent example here on Earth: in the Andes, between the latitudes of 17 and 30 degrees South. These mountains aren't granite, but they are a mix of igneous and meta-igneous rocks, which are similarly crystalline.
The eastern slopes of the mountains is moistened by water that evaporates in the Amazon Basin. The west side is the Atacama Desert. For example, the capital of Bolivia, La Paz, sits in the eastern foothills, and receives 500-600mm of rainfall per year. In contrast, the Chilean city of Arica - only 350km away - receives an average of 0.08mm.
Here's a Google Earth view of the Andes between Arica and La Paz with my pointer on the continental divide (which is not the highest point, as my line coincidentally runs over a summit in Bolivia).
We can immediately zoom in on the effects of precipitation on the mountains.
The highest summits: No precipitation means no glaciation
Fig. 1 is a close-up of two high Andean peaks which appeared in the photo above: the gorgeous, volcanic 6310m Parinaquta on the eastern slopes [Fig. a left], and the rugged 6350m Illimani on the west [Fig. a right].
Illmani has been deeply glaciated, as have most high summits around the world. Its flanks are cut by U-shaped valleys. Its summit is surrounded by steep glacial headwalls. When those headwalls retreat, the summit will collapse.
Parinaquta, in contrast, has clearly never held much ice (though a little snow still clings to the summit - nowhere on Earth is entirely dry). The dominant texture on the mountain is not caused by glacial valleys, but by individual lava flows. The mountain has good radial symmetry, like volcanoes on Mars. It will continue to grow for a long time yet.
Middle elevations: strangely straight channels
Let's take a look at the dry side of the Andes at lower elevations. Fig. b shows a 30-km area located halfway between Parinaquta and Arica.
These channels are quite unusually straight. No quantitative work has been done on these channels to the best of my knowledge (at least in the English scientific literature; Chilean geologists may have done much more).
Morgan et al. (2014) assert that these channels are formed by mud-rich flows. These wet flows are few and far between. The majority of the sediment is moved by air. The wind in the area flows preferentially through the channels, but - unlike the mudflows, or normal rivers - it is driven less by downhill-gradients than by large-scale weather gradients in the area. The wind flows straight, and it straightens the channels. [Morgan et al. also suggest that, during particularly dry periods, the wind may leave channels in inverted relief].
Coastlines: dry climates don't erode much
Your question does not directly mention coastlines, but the dry Arica coast does have one relevant feature: the river mouths do not have noticeable deltas. The volume of a delta is a rough proxy for the rate at which sediment is removed from the mountains upstream and carried out to the ocean, minus the rate at which the ocean carries sediment away from the shore. This proxy has limited value, as it is greatly affected by ocean dynamics, the drainage area of the river, and the presence of a subduction zone near the shore.
Most wet coastlines with subduction zones (such as the coast of Papau New Guinea, Fig. c left) produce enough sediment to maintain estuaries, deltas, or little puffs of sand. In contrast, the rivers near Arica hardly change the shape of the Chilean coastline (Fig. c right).
We can predict that a reduction in total precipitation on the Earth would drastically reduce the average erosion rate on land.
Global changes
Earth, unlike Mars, has active tectonics. Our volcanoes will never grow to the height of Olympus Mons because the continental plates shift beneath them. Yet our mountains now are beset by river incision and by glaciation. Their lifetime is short - perhaps half a billion years, no more, and usually far less. Wind erosion is ~one hundredth the speed of glacial and fluvial erosion. On Dry Earth, a mountain range might survive to be nearly the same age as the planet. If tectonics were to carry on at their usual rate, mountains would soon cover much of the Earth.
Sedimentary rocks would be rarer, and made of baked dust rather than river cobbles or mud. Needles of salt might grow on the plains, if there was enough moisture for the air to carry them.
I imagine Dry Earth as a towering desert, where the lowlands are walled in by the broken remnants of billion-year-old mountain chains, and the dust is made from dark volcanic rock.
