Use your air conditioner. Air conditioning reduces the amount of airborne pollen from trees, grasses and weeds that finds its way indoors. Air conditioning also lowers indoor humidity and can reduce your exposure to dust mites. If you don't have air conditioning, try to keep your windows closed during pollen season.
Decontaminate your decor. Minimize dust that may worsen nighttime symptoms by replacing certain items in your bedroom. For example, encase pillows, mattresses and box springs in dustproof covers. Remove carpeting and install hardwood or linoleum flooring. Use washable curtains and blinds.
Maintain optimal humidity. If you live in a damp climate, talk to your doctor about using a dehumidifier.
Prevent mold spores. Clean damp areas in the bath, kitchen and around the house to keep mold spores from developing. Get rid of moldy leaves or damp firewood in the yard.
Reduce pet dander. If you're allergic to dander, avoid pets with fur or feathers. Having pets regularly bathed or groomed also may reduce the amount of dander in your surroundings.
Clean regularly. Clean your home at least once a week. If you're likely to stir up dust, wear a mask or have someone else do the cleaning.
Cover your nose and mouth if it's cold out.
The symptoms indicate a allergic origin/ hypersensitivity to certain environmental antigen as it has a particular seasonal trend. It is probably the first symptom ( as age mentioned is only 1 year, so I suppose it is the first winter for him) of bronchial asthma.
Bronchial asthma diagnosis is partly clinical ( clinical examination by a doctor) and partly by some tests like chest x ray, absolute eosinophil count, allergy test, pulmonary function test ( can only be done after 3-4 years of age)
Some primary measures you can take
a. Keep the bedroom clean and as much dust free as possible.
b. light plain clothing is better.
c. keep flower vas and other vegetative stuffs away from the child.
d. better to avoid wall hangings, carpets etc which attract dust.
e. strong and pungent odour to be avoided.
f. exposure to sudden extreme temperatures ( both cold and hot) to be avoided.
g. Use mask if any other family member has respiratory infection
last but important thing is bronchial asthma should be treated with proper medications ( inhalers, tablets), but as prescribing medicine is beyond the scope of this area, I would like to advice you to consult a Pediatrician as earliest.