There are cycles under the earth. No not bicycles!
Any repeating sequence of natural events should be helpful to your dwarves.
First thing that came to mind is rainy season. While the rain won't be falling on your dwarves heads, the water will be collecting in the mines and caves. Think of the boys trapped in the Thai caves at the moment. Authorities are worried about the oncoming rainy season flooding the caves.
If snow and ice is the source of your mines water, then spring's winter melt will be the cause of annual fluctuations in water. Even if there is no direct water source above the mines like a rainy season or snowpack you can still have fluctuations. Consider the okavango delta, which is bone dry for part of the year but then receives 11 000 billion litres of water from the Angola Highlands many miles away, not from direct rainfall over the delta itself. It takes a month for the water to travel across 1200 km of land. Now just put all that water in an underground cave system and adjust accordingly.
Secondly, as already mentioned in the comments, tide. I'm not sure how large this will be. It will typically be restricted to water sources connected to the oceans. Internal rivers and lakes don't typically have a noticeable tidal value.
Thirdly, as mentioned by Seserous, animal mating and birthing seasons. I was thinking bats, rodents, and various bugs. If there is a form of cicada in your world, you have a longer "decadal" year marker (I know, on Earth, cicadas repeat on a 7 year cycle).
Temperature doesn't seem to vary much underground, due to season.
The earth temperature beyond a depth of 1 meter is usually insensitive to the diurnal cycle of air temperature and solar radiation and the annual fluctuation of the earth temperature extends to a depth of about 10 meters. In order to study the fluctuations of the ground temperature with depth we have installed a 50m deep U-tube in the ground equipped with thermocouples at various depths. The measured temperatures indicate that the short-period temperature variations are prominent to a depth of approximately 0.5 m. Because of the high thermal inertia of the soil, the temperature fluctuations at the surface of the ground are diminished as the depth of the ground increases. The annual temperature variation of the ground at a depth of 3m is between 15 to 25°C while at a depth of 25m is negligible and the temperature remains constant at about 22°C. The temperature measurements are compared to the calculated values resulting from simulations performed with TRNSYS.
Source. PDF | Annual ground temperature measurements at various depths.
For short time-keeping, I assume some sort of water-based clock would be used. Once a standard measurement of how far a water droplet should drop is defined, they can keep track of seconds. Then they can create minutes using their number system e.g. 60 or 100 seconds etc.
They can also use the classic fantasy time-keeping candle hours based on how long it takes to burn notched candles (these are typically made of standard consistencies and have a known number of hours it will take to burn through. Although this probably is affected by drafts or trimmed wick etc).